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In this paper, we study the cooperative global robust output regulation problem for a class of lower triangular nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model to convert the cooperative global robust output regulation problem into a global robust stabilization problem of a so-called augmented multi-agent system which is in the block lower triangular form. We then further show that, under a set of standard assumptions, the augmented multi-agent system can be globally stabilized via a distributed state feedback control law by developing a block backstepping technique. A special case of the main result of this paper leads to the solution of the leader-following global robust consensus problem for a class of nonlinear uncertain multi-agent systems. [ABSTRACT FROM AUTHOR]

The scenario approach is a general methodology for data-driven optimization that has attracted a great deal of attention in the past few years. It prescribes that one collects a record of previous cases (scenarios) from the same setup in which optimization is being conducted and makes a decision that attains optimality for the seen cases. Scenario optimization is by now very well understood forconvexproblems, where a theory exists that rigorously certifies the generalization properties of the solution, that is, the ability of the solution to perform well in connection to new situations. This theory supports the scenario methodology and justifies its use. This paper considersnonconvexproblems. While other contributions in the nonconvex setup already exist, we here take a major departure from previous approaches. We suggest that the generalization level is evaluated only after the solution is found and its complexity in terms of the length of a support subsample (a notion precisely introduced in this paper) is assessed. As a consequence, the generalization level is stochastic and adjusted case by case to the available scenarios. This fact is key to obtain tight results. The approach adopted in this paper applies not only to optimization, but also to generic decision problems where the solution is obtained according to a rule that is not necessarily the optimization of a cost function. Accordingly, in our presentation we adopt a general stance of which optimization is just seen as a particular case. [ABSTRACT FROM AUTHOR]

The robust control problem of a class of nonlinear systems subject to external disturbances, control gain uncertainty, and nonlinear uncertainties is investigated in this paper using a nonlinearity estimator-based control approach. Different from the existing results, the crucial but highly restrictive hypothesis on the boundedness of nonlinear uncertainties is removed from this paper by means of the tools of semiglobal stabilization. By delicately constructing a specific composite Lyapunov function for the closed-loop system as well as several useful level sets, the rigorous qualitative robustness performance is presented for the closed-loop system. Finally, an example of a single-link manipulator is utilized to demonstrate the performance specification claimed by the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper describes a new paradigm for stock trading involving the use of classical feedback controllers which are “model free” in that they use neither parameterization nor estimation of stock price dynamics. At time $t$, the control signal is the investment level $I(t)$, obtained via a mapping on the so-called gain-loss function $g(t)$. While such strategies fall under the umbrella of technical analysis, our approach differs from the literature in a fundamental way: Whereas existing work in finance involves statistical analysis via historical back-testing, our new control-theoretic paradigm aims to provide “certification theorems” giving conditions under which certain robustness properties are guaranteed with respect to benchmark classes for the time-varying stock price $p(t)$. We demonstrate our ideas using a linear feedback implementation of a new stock-trading scheme called Simultaneous Long-Short. The analysis is carried out in a so-called idealized frictionless market first using smooth prices for pedagogical purposes and then using a more realistic benchmark involving Geometric Brownian Motion. Finally, simulations are given which include real-world implementation issues. [ABSTRACT FROM AUTHOR]

This paper introduces a new, reference trajectory following, sliding-mode control strategy for disturbed discrete-time systems. The strategy uses an external trajectory generator based on a switching type reaching law. The trajectory following strategy not only ensures all the properties of the quasi-sliding-mode as defined by Gao et al., but with a certain choice of the control parameters it also guarantees a significant reduction of the quasi-sliding-mode band width and the errors of all the state variables. This paper also considers the problem of error calculation in the discrete-time, reaching law based sliding-mode control systems. It is shown that the limitation of the sliding variable in the sliding phase directly results in bounded errors of all state variables. The results are verified with a simulation example. [ABSTRACT FROM AUTHOR]

Robustness as a system property describes the degree to which a system is able to function correctly in the presence of disturbances, i.e., unforeseen or erroneous inputs. In this paper, we introduce a notion of robustness termed input-output dynamical stability for cyber-physical systems (CPS) which merges existing notions of robustness for continuous systems and discrete systems. The notion captures two intuitive aims of robustness: bounded disturbances have bounded effects and the consequences of a sporadic disturbance disappear over time. We present a design methodology for robust CPS which is based on an abstraction and refinement process. We suggest several novel notions of simulation relations to ensure the soundness of the approach. In addition, we show how such simulation relations can be constructed compositionally. The different concepts and results are illustrated throughout the paper with examples. [ABSTRACT FROM AUTHOR]

In this paper, we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting, where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function, and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the robustness to model mismatch of a preexisting collocated boundary adaptive feedback law is investigated. This control law was originally designed for an antidamped pure wave partial differential equation (PDE). Actuation and measurements are located at the same boundary. Adaptive terms account for uncertain parameters located at the antidamped boundary, opposite to the collocated actuation and measurement. By extending and transforming the system state using, in particular, backstepping, this paper establishes that this controller is robust to sufficiently small in-domain damping. In particular, both stability and attractivity (convergence) are established similarly as in the nominal case. Note moreover that, assuming that some parameters are known, the exponential stability to an attractor holds. Simulations are performed to illustrate the interest of this study to attenuate mechanical vibrations in an oil-drilling context. [ABSTRACT FROM AUTHOR]

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr {L}_2$ -gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to provide a generalization of the so-called Simultaneous Long–Short (SLS) stock-trading result in the feedback control literature. The significance of the SLS strategy is that it guarantees a “win” in expected value of profits. Whereas previous work involves use of static linear feedback to establish this robust positive expectation property of the gain–loss function, here we obtain the same result for the more general case of PI control. In this SLS setting, robustness is assured with respect to stock prices governed by a Geometric Brownian Motion whose drift and volatility parameters are unknown to the trader. This technical note also includes numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a control technique is presented for an undamped, pinned–pinned Euler–Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances. This is achieved in two main steps. First, a backstepping transformation is used to convert the marginally stable Euler–Bernoulli beam system to a new form that has an exponentially stable homogeneous form. Control inputs are needed to fully convert the system to this form; however, since they are distorted by unknown bounded disturbances, the next step implements a sliding mode controller to account for them. The proposed sliding manifolds require a combination of classical and “second order” techniques in order to avoid discontinuous chattering on the physical system. Therefore, the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate, and do so in the presence of unknown bounded disturbances on the boundary. The main contributions of this paper with respect to previous backstepping designs for the Euler–Bernoulli beam are that all three of the following goals are accomplished together: (i) steady-state position is the origin, (ii) decay rate has no theoretical restrictions, and (iii) is robust to bounded disturbances. [ABSTRACT FROM AUTHOR]

In this paper, a generalized discrete time reaching law for sliding variables with arbitrary relative degree is proposed. The reaching law is based on Gao's strategy and ensures higher order switching-type sliding motion, which is a novel concept in the field of discrete time plants. The controller synthesis process is simplified by performing a specific system state transformation. It is demonstrated that the width of the layer to which the representative point of the system is driven decreases as the relative degree of the sliding variable gets bigger. It has further been proven that achieving a narrower quasi-sliding mode band width is reflected in reduced state error. Finally, the reaching phase elimination for variables with arbitrary relative degree is considered. This is obtained by implementing a time-varying sliding surface in a finite number of initial time instants. Uniform ultimate boundedness of all state variables is guaranteed. [ABSTRACT FROM AUTHOR]

In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities. We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness. The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem. [ABSTRACT FROM AUTHOR]

This paper addresses integral input-to-state stability (iISS) for stochastic nonlinear dynamical systems and develops Lyapunov-type criteria. The developments offer an iISS small-gain framework for verifying robustness of interconnected systems with respect to disturbances. The framework not only includes input-to-state stability (ISS) as a special case, but also highlights fundamental differences between the stochastic and deterministic systems. In particular, dealing with nonlinearities in interconnection gives rise to a unique issue of degradation in the presence of stochastic noises. This paper addresses this issue by coping judiciously with the effect of the gradient of Lyapunov functions of subsystems through diffusion fields in composing a Lyapunov function of the entire system. This paper employs two types of robustness notions, and demonstrates that the influence of the stochastic degradation on one notion is considerably different from the influence on the other notion in dealing with interconnected systems. [ABSTRACT FROM PUBLISHER]

Consider a connected network of agents endowed with local cost functions representing private objectives. Agents seek to find an agreement on some minimizer of the aggregate cost, by means of repeated communications between neighbors. Consensus on the average over the network, usually addressed by gossip algorithms, is a special instance of this problem, corresponding to quadratic private objectives. Consensus on the median, or more generally, consensus on a given quantile, is also a special instance of this problem. In this paper we show that optimizing the aggregate cost function regularized by a total variation (TV) term has appealing properties. First, it can be done very naturally in a distributed way, yielding algorithms that are efficient on numerical simulations. Secondly, the optimum for the regularized cost is shown to be also the optimum for the initial aggregate cost function under assumptions that are simple to state. Finally, these algorithms are robust to unreliable agents that keep injecting some false value in the network. This is remarkable enough, and is not the case, for instance, of gossip algorithms that are entirely ruled by unreliable agents as detailed in the paper. [ABSTRACT FROM PUBLISHER]

In this paper, we study how to utilize forecasts to design online electrical vehicle (EV) charging algorithms that can attain strong performance guarantees. We consider the scenario of an aggregator serving a large number of EVs together with its background load, using both its own renewable energy (for free) and the energy procured from the external grid. The goal of the aggregator is to minimize its peak procurement from the grid, subject to the constraint that each EV has to be fully charged before its deadline. Further, the aggregator can predict the future demand and the renewable energy supply with some levels of uncertainty. We show that such prediction can be very effective in reducing the competitive ratios of online control algorithms, and even allow online algorithms to achieve close-to-offline-optimal peak. Specifically, we first propose a 2-level increasing precision model (2-IPM), to model forecasts with different levels of accuracy. We then develop a powerful computational approach that can compute the optimal competitive ratio under 2-IPM over any online algorithm, and also online algorithms that can achieve the optimal competitive ratio. Simulation results show that, even with up to 20% day-ahead prediction errors, our online algorithms still achieve competitive ratios fairly close to 1, which are much better than the classic results in the literature with a competitive ratio of $e$ . The second contribution of this paper is that we solve a dilemma for online algorithm design, e.g., an online algorithm with good competitive ratio may exhibit poor average-case performance. We propose a new Algorithm-Robustification procedure that can convert an online algorithm with good average-case performance to one with both the optimal competitive ratio and good average-case performance. We demonstrate via trace-based simulations the superior performance of the robustified version of a well-known heuristic algorithm based on model predictive control. [ABSTRACT FROM PUBLISHER]

A model-based event-triggered control scheme for nonlinear constrained continuous-time uncertain systems in networked configuration is presented in this paper. It is based on the combined use of model-predictive control (MPC) and integral sliding-mode (ISM) control, and it is oriented to reduce the packet transmission over the network both in the direct path and in the feedback path, in order to avoid network congestion. The key elements of the proposed control scheme are the ISM local control law, the MPC remote controller, a smart sensor, and a smart actuator, both containing a copy of the nominal model of the plant. The role of the ISM control law is to compensate matched uncertainties, without amplifying the unmatched ones. The MPC controller with tightened constraints generates the control component oriented to comply with state and control requirements and is asynchronous since the underlying constrained optimization problem is solved only when a triggering event occurs. In the paper, the robustness properties of the controlled system are theoretically analyzed, proving the regional input-to-state practical stability of the overall control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to event-triggered control for nonlinear uncertain systems by using the notion of input-to-state stability (ISS) and the nonlinear small-gain theorem. The contribution of this paper is threefold. First, it is proved that infinitely fast sampling can be avoided if the system is input-to-state stabilizable with the sampling error as the external input and the corresponding ISS gain is locally Lipschitz. No assumption on the existence of known ISS-Lyapunov functions is made in the discussions. Moreover, the forward completeness problem with event-triggered control is studied systematically by using ISS small-gain arguments. Second, the proposed approach gives rise to a new self-triggered sampling strategy for a class of nonlinear systems subject to external disturbances. If an upper bound of the external disturbance is known, then the closed-loop system can be designed to be robust to the external disturbance, and moreover, the system state globally asymptotically converges to the origin if the external disturbance decays to zero. Third, a new design method is developed for event-triggered control of nonlinear uncertain systems in the strict-feedback form. It is particularly shown that the ISS gain with the sampling error as the input can be designed to satisfy the proposed condition for event-triggered control and self-triggered control. [ABSTRACT FROM PUBLISHER]

In this paper, we study fundamental properties of minimum inter-event times for several event-triggered control architectures, both in the absence and presence of external disturbances and/or measurement noise. This analysis reveals, amongst others, that for several popular event-triggering mechanisms no positive minimum inter-event time can be guaranteed in the presence of arbitrary small external disturbances or measurement noise. This clearly shows that it is essential to include the effects of external disturbances and measurement noise in the analysis of the computation/communication properties of event-triggered control systems. In fact, this paper also identifies event-triggering mechanisms that do exhibit these important event-separation properties. [ABSTRACT FROM PUBLISHER]

This paper addresses robustness to external disturbances of switched discrete and continuous systems with multiple equilibria. First, we prove that if each subsystem of the switched system is input-to-state stable (ISS), then under switching signals that satisfy an average dwell-time bound, the solutions are ultimately bounded within a compact set. The size of this set varies monotonically with the supremum norm of the disturbance signal. These results generalize existing ones in the common equilibrium case to accommodate multiple equilibria. Then, we relax the (global) ISS conditions to consider equilibria that are locally exponentially stable (LES), and we establish practical stability for such switched systems under disturbances. Our motivation for studying this class of switched systems arises from certain motion planning problems in robotics, where primitive movements, each corresponding to an equilibrium point of a dynamical system, must be composed to obtain more complex motions. As a concrete example, we consider the problem of realizing safe adaptive locomotion of a three-dimensional biped under persistent external force by switching among motion primitives characterized by LES limit cycles. The results of this paper, however, are relevant to a much broader class of applications, in which composition of different modes of behavior is required. [ABSTRACT FROM AUTHOR]

In this paper, a numerically robust solver for least-square problems with bounded variables (BVLS) is presented for applications including, but not limited to, model predictive control (MPC). The proposed BVLS algorithm solves the problem efficiently by employing a recursive QR factorization method based on Gram–Schmidt orthogonalization. A reorthogonalization procedure that iteratively refines the QR factors provides numerical robustness for the described primal active-set method, which solves a system of linear equations in each of its iterations via recursive updates. The performance of the proposed BVLS solver, which is implemented in C without external software libraries, is compared in terms of computational efficiency against state-of-the-art quadratic programming solvers for small- to medium-sized random BVLS problems and a typical example of embedded linear MPC application. The numerical tests demonstrate that the solver performs very well even when solving ill-conditioned problems in single-precision floating-point arithmetic. [ABSTRACT FROM AUTHOR]

In this paper, we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network, composed as a set of linear time invariant systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the individual systems in the network are dissipative with respect to a (nonempty) set of interconnection neutral supply functions. Each supply function from this set is defined on a single interconnection link in the network. Specific characterizations of neutral supply functions are presented, which imply robustness of network stability/dissipativity to removal of interconnection links. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of output tracking with prescribed transient and steady-state performance for strict-feedback systems with unknown nonlinear functions and unmatched disturbances. In lieu of Nussbaum gain techniques, parameter estimation algorithms and switching control strategies, a continuous static low-complexity control solution is provided by means of a novel combination of smooth orientation functions and error transformation functions. The proposed method possesses inherent robustness against model uncertainties, disturbances, and virtual control signal derivatives, thus eliminating the needs to introduce extra robust control schemes and compute analytic derivatives. Comparative simulation results further illustrate the above theoretical findings. [ABSTRACT FROM AUTHOR]

This work deals with the analysis and the design of minimum-time control laws for a class of nonlinear discrete-time dynamical systems characterized by \cal K-continuous transition maps and bounded control inputs. In the paper, it is shown that the reachability properties of the target set, even if not robust positively controllable in one state transition, can be exploited to assess the existence of a robust positively controllable set including the target in its interior. This result allows the formulation of a robustified minimum-time control policy, based on iterated online optimizations and guaranteeing the ultimate boundedness of the state-trajectories in the presence of bounded uncertainties, even if the target set is not robust positively controllable. [ABSTRACT FROM PUBLISHER]

Use of a gradient descent control law has been a popular method to effectively stabilize undirected rigid formations, by assuming that interagent distances between a certain set of neighboring agent pairs can be accurately specified and measured. This paper examines the collective motion behavior for an infinitesimally rigid formation in a three-dimensional ambient space, in the case that neighboring agent pairs have slightly differing views or measurements of the desired interagent distances they are tasked to maintain. It is shown that the formation shape will converge exponentially fast to a rigid one, while additional rigid helical motions of the final formation will occur. We further discuss the convergence to the equilibrium motions, and derive certain motion parameter formulas to describe the rigid formation movements by employing the angular momentum concept from classical mechanics. Finally, we explain how the idea can be used for steering a rigid formation to move as a rigid body. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of asymptotically stabilizing the splay state configuration of a network of identical pulse coupled oscillators through the design of the their phase response function. The network of pulse coupled oscillators is modeled as a hybrid system. The design of the phase response function is performed to achieve almost global asymptotic stability of a set, wherein oscillators’ phases are evenly distributed on the unit circle. To establish such a result, a novel Lyapunov function is proposed. Robustness with respect to frequency perturbation is assessed. Finally, the effectiveness of the proposed methodology is shown in an example. [ABSTRACT FROM AUTHOR]

This paper aims at designing a nonasymptotic and robust pseudo-state estimator for a class of fractional order linear systems which can be transformed into the Brunovsky's observable canonical form of pseudo-state space representation with unknown initial conditions. First, this form is expressed by a fractional order linear differential equation involving the initial values of the fractional sequential derivatives of the output, based on which the modulating functions method is applied. Then, the former initial values and the fractional derivatives of the output are exactly given by algebraic integral formulae using a recursive way, which are used to nonasymptotically estimate the pseudo-state of the system in noisy environment. Second, the pseudo-state estimator is studied in discrete noisy case, which contains the numerical error due to a used numerical integration method, and the noise error contribution due to a class of stochastic processes. Then, the noise error contribution is analyzed, where an error bound useful for the selection of design parameter is provided. Finally, numerical examples illustrate the efficiency of the proposed pseudo-state estimator, where some comparisons with the fractional order Luenberger-like observer and a new fractional order \mathcalH\infty-like observer are given. [ABSTRACT FROM AUTHOR]

Schur-type methods in [6] and [11] solve the robust pole assignment problem by employing the departure from normality of the closed-loop system matrix as the measure of robustness. They work well generally when all poles to be assigned are simple. However, when some poles are close or even repeated, the eigenvalues of the computed closed-loop system matrix might be inaccurate. In this paper, we present a refined Schur method, which is able to deal with the case when some or all of the poles to be assigned are repeated. More importantly, the refined Schur method can still be applied when place [14] and robpole [28] fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom. [ABSTRACT FROM AUTHOR]

In this paper, tools to study forward invariance properties with robustness to disturbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of differential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without disturbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout this paper to illustrate the main ideas. [ABSTRACT FROM AUTHOR]

Although the finite-time control theory and application have been studied very well in the literature, few results are concerned with the effect of sampled-data control. In this paper, first, the stability analysis of a chain of integrators under a discretized finite-time controller is given. Then, in the presence of disturbance, the robustness of the closed-loop system is also investigated. Based on a Lyapunov method, the ultimate bound for the steady states of the considered closed-loop system is estimated. Some simulation and examples are provided to verify the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns the delay margin achievable using proportional-integral-derivative (PID) controllers for linear time-invariant (LTI) systems subject to variable, unknown time delays. The basic issue under investigation addresses the question: What is the largest range of time delay so that there exists a single PID controller to stabilize the delay plants within the entire range? Delay margin is a fundamental measure of robust stabilization against uncertain time delays and poses a fundamental, longstanding problem that remains open except in simple, isolated cases. In this paper, we develop explicit expressions of the exact delay margin and its upper bounds achievable by a PID controller for low-order delay systems, notably the first- and second-order unstable systems with unknown constant and possibly time-varying delays. The effect of nonminimum phase zeros is also examined. PID controllers have been extensively used to control and regulate industrial processes that are typically modeled by first- and second-order dynamics. While furnishing the fundamental limits of delay within which a PID controller may robustly stabilize a delay process, our results should also provide useful guidelines in tuning PID parameters and in the analytical design of PID controllers. [ABSTRACT FROM AUTHOR]

This paper is concerned with the $H_2$ control of linear systems with multiple quantization channels. The quantization parameters of each channel are not required to be identical. The resultant mismatches are represented by polytopic uncertainties. A composite controller composed of linear and nonlinear parts is designed to meet the required $H_2$ performance and offset the quantization error. Resorting to a vertex separation technique and Finsler lemma instead of matrix inverse operations, new synthesis conditions for the desired linear part are derived in terms of linear matrix inequalities, which are further extended to treat systems with norm-bounded uncertainties. A comparison of conservativeness between the proposed methods and the existing ones is demonstrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper proposes distributed algorithms to solve robust convex optimization (RCO) when the constraints are affected by nonlinear uncertainty. We adopt a scenario approach by randomly sampling the uncertainty set. To facilitate the computational task, instead of using a single centralized processor to obtain a “global solution” of the scenario problem (SP), we resort to multiple interconnected processors that are distributed among different nodes of a network to simultaneously solve the SP. Then, we propose a primal-dual subgradient algorithm and a random projection algorithm to distributedly solve the SP over undirected and directed graphs, respectively. Both algorithms are given in an explicit recursive form with simple iterations, which are especially suited for processors with limited computational capability. We show that, if the underlying graph is strongly connected, each node asymptotically computes a common optimal solution to the SP with a convergence rate $O(1/(\sum _{t=1}^k\zeta ^t))$ , where $\lbrace \zeta ^t\rbrace$ is a sequence of appropriately decreasing stepsizes. That is, the RCO is effectively solved in a distributed way. The relations with the existing literature on robust convex programs are thoroughly discussed and an example of robust system identification is included to validate the effectiveness of our distributed algorithms. [ABSTRACT FROM AUTHOR]

The cooperative output regulation (COR) problem of heterogeneous linear multi-agent networks [multi-agent systems (MASs)] is studied in the paper. Agents are allowed to be inherently heterogeneous linear time-invariant systems and the communication graph is not restricted to be acyclic. Both state- and output-feedback control protocols that make use of neighbors’ output information are considered. In light of robust control theory and robust output regulation theory, small-gain solvability conditions with closed-loop pole specifications are first derived. Then, an ${H_{\infty }}$ performance allocation approach is proposed for protocol design, where algorithms for optimizing graph weights and designing protocol gains are constructed, respectively. Both continuous-time (CT) and discrete-time MASs are investigated in a unified framework. In addition, solvability of the COR problem is further discussed from the graph, agent, and exosystem aspects, respectively. It is proved that the proposed approach pre-explicitly ensures the solvability of the COR problem for either of the three cases: the graph is acyclic; for CT MASs, agents are minimum-phase and right-invertible; and for CT MASs, the poles of the exosystem have zero real part and agents are right-invertible. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of robust design problems with polynomial dependence on the uncertainty. One of the main motivations for considering these problems comes from robust controller design, where one often encounters systems that depend polynomially on the uncertain parameters. This paper can be seen as integrated in the emerging area of probabilistic robustness, where a probabilistic relaxation of the original robust problem is adopted, thus requiring the satisfaction of the constraints not for all possible values of the uncertainty, but for most of them. Different from the randomized approach for tackling probabilistic relaxations, which is only guaranteed to provide soft bounds on the probability of satisfaction, we present a deterministic approach based on the novel concept of kinship function introduced in this paper. This allows the development of an original framework, which leads to easily computable deterministic convex relaxations of the probabilistic problem. In particular, optimal polynomial kinship functions are introduced, which can be computed a priori and once for all and provide the “best convex bound” on the probability of constraint violation. More importantly, it is proven that the solution of the relaxed problem converges to that of the original robust optimization problem as the degree of the optimal polynomial kinship function increases. Furthermore, by relying on quadrature formulas for computation of integrals of polynomials, it is shown that the computational complexity of the proposed approach is polynomial in the number of uncertain parameters. Finally, unlike other deterministic approaches to robust polynomial optimization, the number of variables in the ensuing optimization problem is not increased by the proposed approximation. An important feature of this approach is that a significant amount of the computational burden is shifted to a one-time offline computation whose results can be stored and provided to the end-user. [ABSTRACT FROM PUBLISHER]

An introduction to a number of research papers within the issue is presented on topics including optimal dynamic quantizer for nonlinear control systems, robust control in experimental design and synchronization of nonlinear oscillators.

The note considers the problem of computing pure Nash equilibrium (NE) strategies in distributed (i.e., network-based) settings. The paper studies a class of inertial best-response dynamics based on the fictitious play (FP) algorithm. It is shown that inertial best-response dynamics are robust to informational limitations common in distributed settings. Fully distributed variants of FP with inertia and joint strategy FP (JSFP) with inertia are developed and convergence is proven to the set of pure NE. The distributed algorithms developed in the paper rely on consensus methods. Results are validated using numerical simulations. [ABSTRACT FROM AUTHOR]

We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back to the classical tradeoff between convergence rate and delay robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay robustness. Indeed, for such systems, using a backstepping controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence. [ABSTRACT FROM AUTHOR]

Inspired by the interesting findings regarding the hierarchy and coordination of pigeons in Nagy et al.  [Nature, 2010], we revisit the discrete-time leader–follower consensus problem with switching topologies. The purpose of this paper is to investigate the impact of hierarchical topologies and followers’ self-loops on the convergence performance of leader–follower consensus, including the convergence rate and robustness to switching topologies. We first study the fixed topology case, and show that the followers converge to the leader's state in finite time if and only if each follower has no self-loops and the topology is hierarchical. However, we show via counterexample, that leader–follower consensus may not be achieved when some followers have no self-loops and the topology is switching; even if each interaction graph has a spanning tree rooted at the leader. With the aid of binary relation theory, we further develop a new approach to present a novel sufficient condition for leader–follower consensus with switching topologies and with some followers having no self-loops. We prove that when no followers have self-loops and the same hierarchical organization is kept under the switching topologies, then the fastest rate of convergence in leader–follower consensus can be achieved; even in the presence of complex dynamic topologies. This is consistent with the natural phenomena found in pigeons by Nagy et al. [ABSTRACT FROM AUTHOR]

Sliding mode control (SMC), which is known to present strong robustness against various disturbances, has been extensively employed on underactuated systems, whose control problem has been a research focus in recent years. However, though received great attention, the study on SMC for underactuated systems still remains quite open since it is very challenging to construct a proper manifold which can simultaneously stabilize both actuated and unactuated system states. Motivated to promote the corresponding research, we propose an improved second-order SMC (IS-SMC) method for a class of nonlinear underactuated systems in this paper, which guarantees that the closed-loop system's equilibrium point is asymptotically stable even in the presence of unknown nondiminishing disturbances. Different from traditional SMC methods presenting with chattering problem, the control inputs of the proposed method are essentially continuous, which brings much convenience for practical applications. Moreover, for the disturbances which are second-order differentiable, an enhanced IS-SMC (EIS-SMC) method is derived to guarantee the smoothness for both the control inputs and their derivatives. Finally, the proposed approach is applied to a practical underactuated system: The overhead crane system, with sufficient simulation results provided to validate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This technical note proposes a resilient cooperative control design for networked cooperative systems when subjected to external attacks. The systems considered in this paper can have any information topology described by a leader-follower digraph. A potential attack on such systems consists of unknown bounded signals generated from any linear or nonlinear finite- $L_2$ -gain exogenous dynamical system and injected distributively into nodes of the system's network. The purpose of the attack is to destabilize the consensus dynamics by intercepting the system's communication network and corrupting its local state feedback. The proposed resilient control design consists of introducing a virtual system with hidden network such that the overall system consisting of the original consensus system, the virtual system, and the attack dynamics is stable without requiring any information about the locations or nature of the attack. This is accomplished by utilizing the concept of competitive interaction to provide explicit design criteria for the hidden network of the virtual system to interact with the original system. A graph theoretical approach and a Lyapunov direct method are used to analyze the overall system and show that the proposed design ensures stability of the overall system and preserves the consensus of the original system. An example, which includes several scenarios, is used to illustrate the results. [ABSTRACT FROM AUTHOR]

The focal point of this paper is the well known problem of polynomial positivity over a given domain. More specifically, we consider a multivariate polynomial ƒ(x) with parameter vector x restricted to a hypercube X C Rn. The objective is to determine if ƒ(x) > 0 for all x E X. Motivated by NP-Hardness considerations, we introduce the so-called dilation integral method. Using this method, a "softening" of this problem is described. That is, rather than insisting that ƒ(x) be positive for all x ϵ X, we consider the notions of practical positivity and practical non-positivisy. As explained in the paper, these notions involve the calculation of a quantity e > 0 which serves as an upper bound on the percentage volume of violation in parameter space where ƒ(x) ≤ 0. Whereas checking the polynomial positivity requirement may be computationally prohibitive, using our ϵ-softening and associated dilation integrals, computations are typically straightforward. One highlight of this paper is that we obtain a sequence of upper bounds ϵk which are shown to be "sharp" in the sense that they converge to zero whenever the positivity requirement is satisfied. Since for fixed n, computational difficulties generally increase with k, this paper also focuses on results which reduce the size of the required k in order to achieve an acceptable percentage volume certification level. For large classes of problems, as the dimension of parameter space n grows, the required k value for acceptable percentage volume violation may be quite low. In fact, it is often the case that low volumes of violation can be achieved with values as low as k = 2. [ABSTRACT FROM AUTHOR]

By using a delay line as a signal generator, we design a simple robust controller for the approximate regulation (i.e., approximate asymptotic tracking and rejection) of almost periodic signals for linear systems. As opposed to the related existing results, our controller design does not require online parameter tuning. Besides the usual assumptions about stabilizability, detectability, and nonexistence of transmission zeros for the plant, the controller design algorithm of this paper only requires knowledge of the desired tracking accuracy ϵ > 0. Based on this information alone, we can only design a robust controller achieving, in the presence of unknown trigonometric polynomial disturbances and additive perturbations to the plant and the controller, lim supt→ ∞ ∥ y(t) - yref(t) ∥ < ϵ ∥ yref ∥. Here, y is the output of the plant and yref is an arbitrary almost periodic reference signal taken from an infinite-dimensional generalized Sobolev space of almost periodic functions. In this paper, we also study robust output regulation in the limiting case where ϵ → 0. It turns out that, due to the general loss of exponential closed loop stability, asymptotic tracking/rejection can also be lost as ϵ → 0, unless the exogenous signals are smooth enough. This last result extends some recent theorems on (nonrobust) open loop output regulation for infinite-dimensional exosystems. The results of this paper are new and potentially useful for finite-dimensional plants, but the main results are also true for infinite-dimensional systems with bounded control and observation operators. [ABSTRACT FROM AUTHOR]

This paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps, via state feedback control, to a given target set. The assumptions that are made in this paper are that the system is discrete-time, nonlinear and time-invariant and subject to mixed constraints on the state and input. A persistent disturbance, dependent on the current state and input, acts on the system. Existing results are not able to address state- and input-dependent disturbances and the results in this paper are, therefore, a generalization of previously published results. One of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software, provided the system is piecewise affine and the constraints are polygonal. Existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances, whereas the results in this paper remove this limitation. Some simple examples are also given that show that, even if all the relevant sets are convex and the system is linear, convexity of the set of controllable states cannot be guaranteed. [ABSTRACT FROM AUTHOR]

The paper aims to establish a general framework for robust output synchronization of a group of networked agents. The agents under investigation have nonlinear, uncertain and heterogeneous dynamics. Output synchronization denotes that all agents, through collaborative control, achieve output agreement and follow a desired pattern. In particular, the agreed trajectory is not defined by nor known to any agent in advance. Collaborative control is achieved using only output information from neighboring agents. Two concurrent actions are revealed in the proposed synchronization framework. This framework involves design strategies for both perturbed consensus and perturbed regulation problems, subject to a class of small gain conditions. The success of the framework is verified by constructive proof and numerical simulation. [ABSTRACT FROM AUTHOR]

The problem of system diagnosability verification is concerned with whether a fault in the system operation can be diagnosed by using the system model and observations of the system output. In this paper, we investigate the (\deltad,\deltam)-diagnosability of hybrid automata, which characterizes the maximum delay for diagnosing faults since their first occurrence, given the measurement uncertainty in observing the system output. [ABSTRACT FROM AUTHOR]

This paper studies the real-time implementation of distributed controllers on networked cyber-physical systems. We build on the strengths of event- and self-triggered control to synthesize a unified approach, termed team-triggered, where agents make promises to one another about their future states and are responsible for warning each other if they later decide to break them. The information provided by these promises allows individual agents to autonomously schedule information requests in the future and sets the basis for maintaining desired levels of performance at lower implementation cost. We establish provably correct guarantees for the distributed strategies that result from the proposed approach and examine their robustness against delays, packet drops, and communication noise. The results are illustrated in simulations of a multi-agent formation control problem. [ABSTRACT FROM AUTHOR]

This paper formulates and studies the concept of quasi-Disturbance-to-Error Stability (qDES) which characterizes robustness of a nonlinear observer to an output measurement disturbance. In essence, an observer is qDES if its error dynamics are input-to-state stable (ISS) with respect to the disturbance as long as the plant's input and state remain bounded. We develop Lyapunov-based sufficient conditions for checking the qDES property for both full-order and reduced-order observers. We use these conditions to show that several well-known observer designs yield qDES observers, while some others do not. Our results also enable the design of novel qDES observers, as we demonstrate with examples. When combined with a state feedback law robust to state estimation errors in the ISS sense, a qDES observer can be used to achieve output feedback control design with robustness to measurement disturbances. As an application of this idea, we treat a problem of stabilization by quantized output feedback. [ABSTRACT FROM AUTHOR]

In this paper, we study a dissipativity property which was recently used in several results on economic model predictive control to ensure optimal operation of a system at steady-state as well as stability. In particular, we first investigate whether this dissipativity property is not only sufficient, but also necessary for optimal steady-state operation. In the most general case, this is not true; nevertheless, under an additional controllability assumption, we show that dissipativity is in fact necessary. Second, we provide a robustness analysis of the dissipativity property with respect to changes in the constraint set, which can result in a change in the considered supply rate. [ABSTRACT FROM AUTHOR]

In this paper, it is proved that a predictor-based feedback controller can effectively yield asymptotic convergence for a class of linear systems subject to input-dependent input delay. This class is characterized by the delay being implicitly related to past values of the input via an integral model. This situation is representative of systems where transport phenomena take place, as is frequent in the process industry. The sufficient conditions obtained for asymptotic stabilization bring a local result and require the magnitude of the feedback gain to be consistent with the initial conditions scale. Arguments of proof for this novel result include general Halanay inequalities for delay differential equations and build on recent advances of backstepping techniques for uncertain or varying delay systems. [ABSTRACT FROM PUBLISHER]