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This paper is based on our paper [15]. We present the main results; the verbatim proofs are omitted due to the page limitation. We develop large deviations principles for systems driven by continuous-time Markov chains with two-time scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of two-time-scale formulation stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Then the results are applied to certain dynamic systems and LQ control problems.

This paper investigates the dynamics of networks of systems achieving rendezvous under linear quadratic optimal control. While the dynamics of rendezvous were studied extensively for the symmetric case, where all systems have exactly the same dynamics (such as simple integrators), this paper investigates the rendezvous dynamics for the general case when the dynamics of the systems may be different. We show that the rendezvous is stable and that the post-rendezvous dynamics of the network of systems is entirely defined by the common eigenvalues with common eigenvectors output image. The approach is also extended to the case of constraints on systems states, inputs, and outputs.

This paper summarizes what have been done in our recent paper [24], which is concerned with stability of a class of switching jump-diffusion processes. The motivation of our study stems from a wide range of applications in communication systems, flexible manufacturing and production planning, financial engineering, and economics. A distinct feature of the system given by (X(t), α(t)) is the switching process α(t) depends on X(t). This paper focuses on the long-time behavior, namely, stability of the switching jump diffusions. First, the definitions of regularity and stability are recalled. It is then shown that under suitable conditions, the underlying systems are regular or no finite explosion time. To study stability of the trivial solution (or the equilibrium point 0), systems that are linearizable (in the x variable) in a neighborhood of 0 are considered. Sufficient conditions for stability and instability are obtained. Then, almost sure stability is examined by treating Liapunov exponent. The stability conditions present a gap for stability and instability owing to the maximum and minimal eigenvalues associated with the drift and diffusion coefficients. To close the gap, a transformation technique is used to obtain a necessary and sufficient condition for stability.

Real graph Laplacians are of great importance in consensus of multi-agent systems. This paper introduces complex graph Laplacians as a new tool to study the formation control problem in the plane. It is shown that complex graph Laplacians are of equally great importance for planar formation control like real Laplacians for consensus. First, complex graph Laplacians are used to characterize planar formations under given topology of networked agents. Second, complex graph Laplacians are used to derive local and distributed control strategies for asymptotically achieving formations. This paper explores the relations between graph topology, complex Laplacians, and planar formations, and obtains several graphical and algebraic conditions for realizability of spatial formations. Both simulation and experiment results are provided to illustrate our results.

The present work reports a sufficient condition for the consensus of a network of nonidentical Euler-Lagrange (EL) systems with variable time-delays in the communications. The EL-systems are controlled by simple Proportional plus damping (P+d) schemes and the interconnection network is modeled as an undirected weighted graph. Additionally, for the case without delays, the paper reports a new Strict Lyapunov Function (SLF) for the closed-loop system. Experimental evidence, using three 3-Degrees-of-Freedom manipulators interconnected through the Internet, support the theoretical results of this paper.

This paper studies the stability of linear systems with uncertain parameters in the state matrix. Instead of arguing for the worst case like in the classical robust stability methods, we make use of the statistical information on these uncertain parameters, which can be obtained statistically from manufacturing data. Hence, this paper follows the idea of probabilistic robust control and investigates the stability of linear systems with random parameters of known distributions. A sufficient condition for the asymptotic stability in moments is obtained using the generalized Polynomial Chaos expansion theory. Furthermore, to gain more insights on the effects of the random parameters on stability, a special case of uniform distribution is discussed. Finally, the paper concludes with illustrative examples and remarks on future work.

The framework of empirical evidence equilibrium (EEE) for stochastic games is developed in this paper. In a stochastic game, agents collectively influence the dynamic of the environment. In standard equilibria, each agent's strategy is optimal with respect to its opponents' strategies. Therefore, each strategy is the solution to a partially observable Markov decision process (POMDP). The following considerations motivate the notion of EEE. First, solutions to a POMDP can be prohibitively complex to compute and implement. Second, agents might not fully understand the environment's dynamic. Third, standard equilibria do not accommodate different levels of bounded rationality among agents. Finally, reaching equilibrium in stochastic games has not been adequately addressed. In the EEE framework, each agent formulates a simple model of its opponents' effects. It neglects that agents are mutually dependent through the environment and computes an optimal strategy associated with its model. The agents play their strategies against each other and make some observations. Agents are in EEE when the models are consistent with these empirical observations. In this paper, the notion of EEE is formalized and an existence result is established in a general setting. Relations with other equilibria, including mean field equilibria, are also presented. Finally, the learning of EEEs by simple adaptive processes is illustrated through simulation.

In this paper we consider the finite-time stability (FTS) problem for linear time varying systems. In most of the previous literature, the definition of FTS exploits the standard weighted quadratic norm to define the initial and trajectory domains, which, therefore, turn out to be ellipsoidal; this is consistent with the fact that quadratic Lyapunov functions are used to derive the FTS conditions. Conversely, the recent paper [1], considers the case where the above domains are polytopic and, consequently, the analysis is performed with the aid of polyhedral Lyapunov functions. In the current work, the class of Piecewise Quadratic Lyapunov functions is considered. First, it is shown that such class of functions recovers as particular cases both quadratic and polyhedral Lyapunov functions; then a novel sufficient condition for FTS of linear time-varying systems is provided. A procedure is proposed to convert such condition into a computationally tractable problem. The examples illustrated at the end of the paper show the benefits of the proposed technique with respect to the methodologies available in the literature.

This paper explores the relationship between the structure of a network of agents and how efficiently they can learn a common unknown parameter. Agents repeatedly make private observations which are possibly informative about the unknown parameter; they also communicate their beliefs over the set of conceivable parameter values to their neighbors. It has been shown that for agents to learn the realized state, it is sufficient that they incorporate in their beliefs their private observations in a Bayesian way and the beliefs of their neighbors using a fixed linear rule. In this paper we establish upper and lower bounds on the rate by which agents performing such an update learn the realized state and show that the bounds can be tight. These bounds enable us to compare efficiency of different networks in aggregating dispersed information. Our analysis yields an important insight: for agents in large balanced networks learning is much slower compared to that of a central observer regardless of the distribution of information in the network, whereas unbalanced networks result in near efficient learning if the observations of the centrally positioned agents are much more informative than others' observations.

This paper extends the quotient method proposed in [1] and applies it to stabilize a “ball-on-a-wheel” system. The quotient method requires a diffeomorphism to obtain the normal form of the input vector field and uses canonical projection to obtain the quotient. However, the whole process can be done without computing the normal form, which requires defining a quotient generating function and a quotient bracket. This paper presents the steps necessary to apply the quotient method without obtaining the normal form. Furthermore, a Lyapunov function is introduced to prove stability. This paper also presents the experimental implementation of the quotient method to stabilize a ball-on-a-wheel system.

This paper optimizes the number of sensors and their locations for estimating the 2-D spatio-temporal temperature dynamics in large battery packs. Monitoring temperature in battery packs is crucial for safety, efficiency, and longterm endurance. The temperature dynamics in large battery packs evolve in space and time, whereas sensors only provide pointwise data. Moreover, the number of sensors should be minimized to reduce costs. The temperature dynamics are modeled by a system of linear two-dimensional heat partial differential equations (PDEs). In this paper we perform eigende-composition of the PDEs to produce a finite-dimensional model. Modal observability is defined from the magnitude of these eigenmodes. The process of optimizing the number and location of sensors involves two steps: First, a binary optimization minimizes the number of sensors. Second, a constrained nonlinear programming problem is solved to optimize the previously found sets with respect to a min-max-type objective function. The optimization procedure is independent of the estimator design.

The estimation of nonlinear models can be a challenging problem, in particular when the number of available data points is small or when the dimension of the regressor space is high. To meet these challenges, several dimension reduction methods have been proposed in the literature, where a majority of the methods are based on the framework of inverse regression. This allows for the use of standard tools when analyzing the statistical properties of an approach and often enables computationally efficient implementations. The main limitation of the inverse regression approach to dimension reduction is the dependence on a design criterion which restricts the possible distributions of the regressors. This limitation can be avoided by using a forward approach, which will be the topic of this paper. One drawback with the forward approach to dimension reduction is the need to solve nonconvex optimization problems. In this paper, a reformulation of a well established dimension reduction method is presented, which reveals the structure of the optimization problem, and a convex relaxation is derived.

A new architecture for model-based control of unstable and uncertain systems with network induced delays, and for set-point tracking over networks, is presented in this paper. This setup provides better performance than similar approaches in terms of steady-state tracking error and reduction of network traffic by transmitting measurement updates only when necessary. The results in this paper also extend previous work using the Model-Based Networked Control Systems (MB-NCS) approach to consider the output feedback case and to consider models and uncertain systems which do not necessarily have the same dimension; that is, both the parameters and the order of the system are unknown. The Model-Based Event-Triggered (MB-ET) framework presented in this paper is used for stabilization and tracking of piece-wise constant signals and it is extended in two directions; first, to consider a more general two channel networked system and second, to address the reference input tracking problem in the presence of network induced delays.

In this paper we revisit the problem of automatically synthesizing control software enforcing formal specifications given in temporal logic. Existing approaches to solve this problem rely on the explicit or implicit construction of finite abstractions of control systems. Unfortunately, the existing abstraction techniques do not scale beyond a small number of state variables. The objective of this paper is to scale up the construction of such abstractions by focusing on linear control systems and safety specifications. In this more restricted scenario the controller synthesis problem can be reduced to the computation of control invariant subsets. Hence, we focus on the control invariance problem and propose a computational technique exploiting controllability. We illustrate the proposed methods on several synthetic examples illustrating the computational limits of our algorithm.

In this paper, we extend the results of the previous paper in the 2011 American Control Conference into a more general case. In the previous literature, the topologies for the velocity and position are assumed to be the same. However, in some cases, both topologies are different, even one of them is disconnected, due to a different detection technique. Therefore in this paper, we investigate the topological heterogeneity for the formation control and synchronization protocols. The requirement of connectivity for both topologies is relaxed. Since the choice of the topology in this case is much more available than that of the connected topology, now the question is which one is the best combination of the position and velocity topologies? Here we propose an optimization problem for choosing the topology by considering the tradeoff between the communication cost and convergence rate. To solve this optimization problem numerically, an adjusted binary particle swarm optimization algorithm is developed. Finally, some simulation results are provided to verify our formation and synchronization protocols.

This paper investigates the cluster consensus control for generic linear multi-agent systems (MASs) under directed interaction topology via distributed feedback controller. Focus of this paper is particularly on addressing the following problem which is of both theoretical and practical interests but have not been considered in the existing literature: under what kind of interaction among the clusters can the cluster consensus control be achieved regardless of the magnitude of the coupling strengths among the agents? Directed acyclic interaction topology among the clusters is proved to have this property. Our results are proved to be applicable to tackle similar problem arising in cluster consensus of integrator agents, in which to reach the cluster consensus the interaction topology of each cluster is only required to have a spanning tree. Conditions for guaranteeing the cluster consensus control are presented in terms of purely the structure of the interaction topology and thus are very easy to be verified.

In this paper, we develop randomized and deterministic algorithms for computing the probabilistic radius of information associated to an identification problem, and the corresponding optimal probabilistic estimate. To compute this estimate, in the companion paper [11] the concept of optimal violation function is introduced. Moreover, for the case of uniform distributions, it is shown how its computation is related to the solution of a (quasi) concave optimization problem, based on to the maximization of the volume of a specially constructed polytope. In this second paper, we move a step further and develop specific algorithms for addressing this problem. In particular, since the problem is NP-hard, we propose both randomized relaxations (based on a probabilistic volume oracle and stochastic optimization algorithms), and deterministic ones (based on semi-definite programming). Finally, we present a numerical example illustrating the performance of the proposed algorithms.

In this paper the interconnected fractional order systems (FOSs) stabilization problem is studied. For the purpose of stabilization, this paper introduces the Fractional Order-Sliding Mode Observer (FO-SMO). Considering the nonlinear interconnections among the fractional order subsystems that are unknown, but norm bounded, the FO-SMO is employed to estimate the unknown states. Using the observer-based control, asymptotic stabilization is achieved.

In this paper the problem of generating zero error steady-state responses is addressed for a class of hybrid linear systems whose jumps are determined by time only. The procedure for the design of an automatic device generating the steady-state response and input is described. Once such device and a compensator ensuring incremental stability (see the companion paper) are available, the classical output regulation problem for the same class of hybrid linear systems can be immediately solved. Compared with previously available results, no assumption is needed on the plant about minimum phaseness, relative degree or squareness (same number of inputs and outputs). The key role of the zero dynamics and of the additional inputs (when the plant is fat) is highlighted.

Singular Perturbation Margin (SPM) is a stability margin for Nonlinear (NL) systems established from the view of the singular perturbation (time-scale separation) parameter. This paper provides two SPM assessment methods: quantitative and qualitative methods for Linear Slowly Time-Varying (LSTV) systems. Quantitative method offers a more accurate estimated SPM than the qualitative method, while the latter is more insightful for the system analysis, and will be helpful for the SPM gauge design in the future. The effectiveness of the two methods is shown by a gain scheduling design example. The results in this paper could also be extended to nonlinear slowly time-varying systems by its linearization thereof.

This paper investigates necessary conditions for robustness of Markov jump linear systems. It is proven that the version of the small-gain theorem available in the current literature of this class of systems may sometimes yield an arbitrarily conservative robustness margin. Such conservatism, which does not exist in the classical linear time-invariant or linear stochastic scenarios, indicates a general lack of knowledge on how robust Markov jump linear systems can be, at least from the viewpoint of the scaling techniques currently available in the literature. A key step in the paper is the introduction of adjoint LMIs which, in the same situation, attain the maximal degree of robustness. In addition, a spectral approach is proposed and its effectiveness is investigated. An exact characterization for the stability radii is also given in the scalar case.

This paper proposes a filtered-error-based method for a class of nonlinear systems with nonsmooth nonlinearities. For a class of special nonsmooth nonlinearities arising from hysteresis phenomena, a model based on play-like operators to describe the nonlinearities is first reviewed, and then an attempt is made to mitigate the effects of the nonlinearities with available control techniques. A simple filtered-error-based control scheme is specifically developed to guarantee the stability of the adaptive system and ensure tracking error within a desired precision. Simulation results attained for a nonlinear system are given to illustrate and further validate the effectiveness of the proposed methods of this paper.

This paper is concerned with finding the right inverse for the discrete time systems with flat rectangular transfer function matrix and individual channel power constraints. Such problem arises from various areas in control, signal processing and telecommunications. The difficulty of the problem stems from the complexity in obtaining a convex expression of the individual channel power constraints in the state space. This paper solves this problem by converting the constraints to nonlinear matrix inequalities and then linear matrix inequalities, and derives an effective method for computing the optimal right inverse system that simultaneously maximizes the gain coefficient and satisfies the individual channel power constraints. An application example is presented to show the effectiveness and advantage of the derived method and its usefulness in solving real application problems.

This paper deals with the design of experiments for the validation of a class of interval dynamic models. Set-membership algorithms based on interval analysis often allow the computation of guaranteed bounds (e.g. reach tubes, bounds for some estimates) enclosing all the possible scenarios according to some model where uncertainties are specified in a bounded error context. The guarantee of inclusion is very useful to ensure a complete coverage of all the specified scenarios in verification problems (e.g. verification of safety properties). However, such a guarantee and, consequently, the verified properties hold in practice only up to the validity of the considered uncertain model. In addition, the practical validation of dynamic interval models involving bounded uncertain inputs is quite difficult since finding a relevant input excitation leading to some worst-case scenario (e.g. an output reaching its maximum or minimum admissible value at a given time instant) is not a trivial task in general. The current paper proposes a constructive method to generate such worst-case input signals based on the guaranteed sampling of linear interval predictors with non-held uncertain inputs. The results are then illustrated through the example of designing worst-case road profiles to validate the interval model of a quarter vehicle suspension.

The graph topology plays a central role in characterizing the robustness of feedback systems. In particular, it provides necessary and sufficient conditions for the transfer matrix of a stabilized closed-loop system to be continuous with respect to the controller. If in addition we confine our attention to a compact set of controllers, we can draw much stronger conclusions, for example, the uniform continuity of the closed-loop transfer matrix. This motivates a detailed study of convergence in the graph topology, and a characterization of compactness in this topology. Readily verifiable necessary and sufficient conditions for a set (of controllers) to be compact the graph topology are not available at present. Following our preliminary results in an earlier paper, the present paper gives a simple characterization of convergence in the graph topology in the field of fractions associated with the disc algebra. The result is then applied to characterize compact sets in the graph topology in the field of fractions associated with the disc algebra. An application to the problem of approximate system design is also discussed.

Recently, Model Predictive Control (MPC) for buildings has undergone an intensive research. Usually, according to the international standards, a static range for the air temperature represents the thermal comfort which is being kept making use of MPC while minimizing the energy consumption. On contrary, this paper deals with the optimization of the trade-off between energy consumption and Predicted Mean Vote (PMV) index which, opposed to the static temperature range, describes user comfort directly. PMV index is a nonlinear function of various quantities, which makes the problem more difficult to solve. The paper will show the main differences in MPC problem formulation, propose a tractable approximation strategy and compare the control performance both to the conventional and typical predictive control strategies. The approximation of PMV computation will be shown to be sufficiently precise and moreover, such a formulation keeps the MPC optimization problem convex. Finally, it will be shown that the proposed PMV based optimal control problem formulation shifts the savings potential of typical MPC by additional 10% while keeping the comfort at a desired level.

The subject of this paper is the homotopy continuation method (HCM) for solving basic motion planning problems. The validity of the HCM has been demonstrated for driftless control-affine systems belonging to a special class. In this paper, we study the validity of the HCM for control-affine systems with drift. A crucial step in the validation process is to establish a certain sublinear growth condition. Here we derive a set of general conditions which ensure that such a growth condition holds.

This paper advocates that the convergent systems property and incremental stability are two intimately related though different properties. Sufficient conditions for the convergent systems property usually rely upon first showing that a system is incrementally stable, as e.g. in the celebrated Demidovich condition. However, in the current paper it is shown that incremental stability itself does not imply the convergence property, or vice versa. Moreover, characterizations of both properties in terms of Lyapunov functions are given. Based on these characterizations, it is established that the convergence property implies incremental stability for systems evolving on compact sets, and also when a suitable uniformity condition is satisfied.

This paper develops a framework of a robust stability analysis approach called discrete-time noncausal linear periodically time-varying (LPTV) finite impulse response (FIR) scaling. This approach is an extension of (frequency-dependent) causal linear time-invariant FIR scaling, obtained by further introducing time dependence through lifting treatment. This paper first provides a theoretical result showing how such newly introduced time dependence contributes to reduction of conservativeness of robust stability analysis. We further provide linear matrix inequality conditions for robust stability and develop an explicit and feasible numerical method by exploiting noncausal LPTV FIR scaling. The effectiveness of this scaling approach is demonstrated and the above theoretical result is confirmed through numerical examples.

This paper considers the topic of state estimation for the Stochastic Hybrid System (SHS). The SHS is a class of dynamical systems which can accurately describe many interacting continuous and discrete dynamics. State estimation for the SHS, also called hybrid estimation, is an important yet challenging problem. While most previous research has addressed the hybrid estimation for some special classes of the SHS, this paper solves this problem for the general SHS which is a class of continuous-time stochastic processes defined on a hybrid state space. The major contribution of this paper is the proposal of dynamical filtering equations for hybrid estimation. With a given sequence of noisy observations, the filtering equations describe the evolution of the probability distribution function (pdf) of the estimated hybrid state.

As an extension of the robust H ∞ method, the time domain design based on linear matrix inequalities (LMI) presented in [10] is an appealing and conceptually simple framework to obtain robust LPV controllers, however, the resulting controller is not always suitable for implementation. This paper shows that in a variant of the S-procedure how the multiplier is transformed if the parameter domains are related through a Mobius transform. Based on this result, if certain conditions are fulfilled, the paper provides a numerical reliable method to compute and parametrize all the scheduling variables of the LPV controllers that correspond to a given multiplier matrix and can be expressed in terms of the scheduling variables of the plant.

This paper studies relationships, implications, and applications of diagonal stability and D-stability. Necessary and sufficient conditions for continuous- and discrete-time D-stability are presented in terms of structured singular values of related matrices. It is shown that, for a certain class of interconnected systems, diagonal stability and D-stability are equivalent and the optimization of diagonal scaling gives a necessary and sufficient condition for stability of those systems. This paper also discusses several issues on diagonal stability and additive D-stability with their applications to robust optimal power distribution control and stability analysis of a certain class of reaction-diffusion systems with which the proposed robust stability and stabilizing conditions are illustrated. The resultant analysis and control design problems are formulated as linear or semidefinite programs.

This paper investigates the problem of robust H; ∞ filtering for uncertain two-dimensional (2-D) discrete systems in the Fornasini-Marchesini local state-space (FM LSS) model with polytopic uncertain parameters. The goal of the paper is to design filters such that the finite frequency (FF) H; ∞ norm of the filtering error system has a specified upper bound for all uncertainties. A generalized bounded real lemma (BRL) is first derived for FF H; ∞ performance analysis of nominal 2-D FM LSS systems, and then a method, in terms of solving optimization problems with LMI constraints, is presented for robust FF H; ∞ filter analysis and design. An illustrative example is given to show the improvements of the proposed filter design methods.

This paper investigates pose synchronization on the Special Euclidean group SE(3). We first introduce a passivity-based distributed velocity input law to achieve pose synchronization presented in our previous works, where the velocity input partially makes use of absolute pose information to cancel the coupling term between position and orientation. In this paper, we present a new velocity input based only on relative pose information and conduct convergence analysis based on stability of perturbed systems. Moreover, we show a necessary and sufficient condition in terms of interconnection topologies for pose synchronization on SE(3). We finally demonstrate the effectiveness of the present velocity input through simulations.

The aim of this paper is to shed light on how the social relationships between individuals influence their opinions in the case of structurally balanced social networks. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends. A classical example of this situation is a two-party political system. The paper studies the process of opinion forming on such a social community, starting from the observation that the property of structural balance is formally analogous to the monotonicity property of dynamical systems. The paper shows that under the assumption that individuals are positively influenced by their friends and negatively influenced by their enemies, monotone dynamical systems, due to their order-preserving solutions, are natural candidates to describe the highly predictable process of opinion forming on structurally balanced networks.

The moving horizon estimation (MHE) problem is investigated in this paper for a class of networked systems with packet dropouts. The packet dropout is described by a binary switching random sequence. The main purpose of this paper is to design a estimator such that, for all possible packet dropouts, the state estimation error sequence is convergent. By choosing a stochastic cost function, the optimal solution of the MHE optimization problem with packet dropouts is given. Moreover, the convergence properties of the estimator are studied, and the maximum packet dropout probability is given to ensure the convergence of the state estimation error. Finally, the performance of the proposed estimator is evaluated and an example is given to demonstrate the effectiveness of the proposed method.

This paper considers the stabilization problem for nonlinear retarded systems. The author has already proposed a finite spectrum assignment method for nonlinear retarded systems by extending the finite spectrum assignment for linear systems over commutative rings. In this paper, introducing a state predictor based on anticipating synchronization, we propose a new stabilization technique for nonlinear retarded systems. The effectiveness of the proposed control scheme is illustrated by a numerical simulation.

The Tsypkin and Jury-Lee criteria are commonly used to analyse the absolute stability of discrete-time Lur'e systems with slope-restricted nonlinearities. In this paper, we construct a corresponding linear matrix inequality (LMI) condition for the Jury-Lee criterion most appropriate for monotonic, slope-restricted nonlinearities. The corresponding Lur'e-Lyapunov function is also constructed and, via the Lyapunov method, the conditions on the aforementioned criterion are relaxed. The result is explicitly compared with improved LMI-based criteria in the literature. The resulting multiplier from the criterion is also shown to satisfy the conditions of the Zames-Falb multipliers in discrete-time. This indirectly provides a convex search over a subset of the discrete-time Zames-Falb multipliers. Some numerical examples for SISO and MIMO cases are provided to compare the performance of the criteria with existing results, and we demonstrate that the result in this paper provides significant improvement.

This paper presents a robust optimal controller design for unknown nonlinear systems from a perspective of robust adaptive dynamic programming (robust-ADP). The proposed methodology has several novel features. First, the class of nonlinear systems studied in the paper allows for the presence of dynamic uncertainties with unmeasured state and uncertain system order/dynamics. Second, in the absence of the dynamic uncertainty, the online policy iteration technique developed in this paper can be viewed as an extension of the existing ADP method to affine continuous-time nonlinear systems with completely unknown dynamics. Third, the theory of approximate/adaptive dynamic programming (ADP) is integrated for the first time with tools from modern nonlinear control theory, such as the nonlinear small-gain theorem, for robust optimal control design. It is shown that, with appropriate robust redesign, the robust-ADP controller asymptotically stabilizes the overall system. A practical robust-ADP-based online learning algorithm is developed in this paper, and is applied to the robust optimal controller design for a two-machine power system.

This paper presents a method for determining all stabilizing fractional-order (FO) proportional-integral-derivative (PID) controllers that satisfy an H ∞ weighted-sensitivity constraint for a system of integer or non-integer order. All the parameters of such FO PID controllers are calculated in the frequency domain and are given in terms of the proportional gain K p , integral gain K i , and derivative gain K d . In this paper, they will be plotted on the (K p , K i ), (K p , K d ), and (K i , K d ) planes. In particular, this approach provides all the possible values of the gain parameters of the FO PID controllers that satisfy a given weighted-sensitivity condition even when the transfer function of a system is not available, as long as the frequency response thereof can be obtained. An example is given by way of illustrating the usefulness and effectiveness of the method.

This paper presents a new observer for Ito stochastic nonlinear systems with guaranteed stability. Contraction analysis is used to analyze incremental stability of the observer for an Ito stochastic nonlinear system. A bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of contraction rate and maximum noise intensity. The observer design is based on non-unique state-dependent coefficient (SDC) forms which parametrize the nonlinearity in an extended linear form. In this paper, a convex combination of several parametrizations is used. An optimization problem with state-dependent linear matrix inequality (SDLMI) constraints is formulated to select the free parameters of the convex combination for achieving faster convergence and robustness against disturbances. Moreover, the L 2 norm of the disturbance and noise to the estimation error is shown to be finite. The present algorithm shows improved performance in comparison to the extended Kalman filter (EKF) and the state-dependent differential Riccati equation (SDDRE) filter in simulation.

This paper presents a controller synthesis method to stabilize piecewise-affine (PWA) slab systems based on invariant sets. Inspired by the theory of sliding modes, sufficient stabilization conditions are cast as a set of Linear Matrix Inequalities (LMIs) by proper choice of an invariant set which is a target sliding surface. The method has two steps: the design of the attractive sliding surface and the design of the controller parameters. While previous approaches to PWA controller synthesis are cast as Bilinear Matrix Inequalities (BMIs) that can, in some cases, be relaxed to LMIs at the cost of adding conservatism, our method leads naturally to a convex formulation. Furthermore, the LMIs obtained in this paper have lower dimension when compared to other methods because the dimension of the closed-loop state space is reduced. A numerical example on flutter suppression is included to demonstrate the effectiveness of the approach.

In this paper we propose an algorithm for constructing non-asymptotic confidence regions for parameters of general linear systems under mild statistical assumptions. The constructed regions are centered around the prediction error estimate and are guaranteed to contain the “true” parameter with a user-chosen exact probability. Our main assumption is that the noise terms are independent and symmetrically distributed about zero, but they do not have to be stationary, nor do their variances and distributions have to be known. The construction of the region is based on the uniform ordering property of some carefully selected sign-perturbed sums (SPS) which, as we prove, rigorously guarantees the confidence probability for every finite dataset. The paper also investigates weighted estimates and presents a simulation example on an ARMA process that compares our exact confidence regions with the approximate ones based on the asymptotic theory.

This paper is concerned with a nonlinear extension of the author's former result on balanced realization and model order reduction for feedback interconnected systems. This paper proposes novel notions of subspace balanced realization, subspace singular values and subspace singular vectors. They characterize the balanced realization of a subsystem with respect to an input-output map of the whole feedback system. Balanced truncation based on the proposed subspace balanced realization gives us a reduced order subsystem in such a way that the reduced feedback system maintains its stability. It can be readily applicable to a controller reduction problem.

This paper presents a new robust sliding mode control (SMC) method for uncertain stochastic systems with time-varying delay, structural uncertainties and the Brownian noise. The proposed method applies singular value decomposition (SVD) to all the structural uncertainties, and introduces adjustable parameters for control design. Then, a less-conservative condition of robust stability and new robust controller for the uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The reachability of system states to the SMC switching surface is guaranteed by the proposed control rule. It is theoretically proved that the conservatism of the proposed method is less than the previous methods. The simulation demonstrates the correctness of the results.

This paper addresses the problem of characterizing a switching strategy for stabilization of switched linear stochastic systems with state-dependent noise. The strategy is based on the determination of a minimum dwell time. Sufficient conditions that assure exponential mean square stability and a guaranteed cost-to-go performance index are established by analyzing the time evolution of the second-order moment of the state and constructing a novel cross-monotonicity condition at the switching instants, respectively. Alternative conditions are derived for numerical implementations. The proposed method is illustrated by numerical simulations.

A property for a class of systems is said to be structural if it is met by any system in the class regardless of the adopted parameters. In this paper we investigate the structural nature of oscillatory behaviors, adaptation and monotonicity in a class of sign-invariant systems, capturing a wide variety of biological models. We employ standard robustness analysis tools, suitably tailored to the category of sign definite dynamics, i.e. in which terms are monotonic with respect to all arguments. In particular, our results are based on Jacobian analysis and invariant sets, and we are able to provide simple criteria to determine whether a system structurally admits Hopf-type bifurcations, perfect adaptation or monotonic behavior. Such criteria are easily verified numerically on a set of examples.

An earlier investigation on leader-follower consensus protocols for double integrators with multiple time delays [1] is revisited in this paper from two completely different and novel perspectives. First, the crucial stability analysis of time delayed system is replaced with a recent technique called the Cluster Treatment of Characteristic Roots (CTCR). CTCR paradigm is pursued after a block-diagonalization (mode decoupling) transformation on the system. This treatment produces the unique exact and exhaustive stability tables for the dynamics in the space of the delays. Secondly, the novel concept of Spectral Delay Space is presented, as an overture to the CTCR for the determination of the needed potential stability crossing (switching) hypersurfaces in the delay space. Example cases are provided to display the strengths, efficiency and explicitness of this new stability analysis mechanism.

We consider the problem of estimation from noisy relative measurements in a network. In previous work, a distributed scheme for obtaining least-squares (LS) estimates was developed based on the Jacobi algorithm; in a synchronous version, the algorithm was shown to converge exponentially and bounds on the rate of convergence have been obtained. In this paper, we design and analyze a new class of distributed asynchronous smoothing algorithms based on a randomized version of Kaczmarz algorithm for solving linear systems. One of the proposed schemes applies Randomized Kaczmarz directly to the noisy linear system, whereas the other one operates on the normal equations for LS estimation. We analyze the expected convergence rate of the proposed algorithms depending solely on properties of the network topology. Inspired by the analytical insights, we propose a distributed smoothing algorithm, namely Randomized Kaczmarz Over-smoothing (RKO), which has demonstrated significant improvement over existing protocols in terms of both convergence speedup and energy savings.

In this paper we provide two small-gain theorems for impulsive systems. The first of them provides a construction of an ISS-Lyapunov function for interconnections of impulsive systems if ISS-Lyapunov functions for subsystems are given and a small-gain condition holds. If, in addition, these given ISS-Lyapunov functions are exponential then the second theorem provides a construction of an exponential ISS-Lyapunov function for the interconnection if the gains are power functions.