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Existing results on cooperative control of multiagent systems with unknown control directions require that the underlying topology is either fixed with a strongly connected graph or switching between different strongly connected graphs. Furthermore, in most cases the graph is assumed to be balanced. This paper proposes a new class of nonlinear proportional-integral (PI) based algorithms to relax these requirements and allow for unbalanced and switching topologies having a jointly strongly connected basis. This is made possible for single-integrator (SI) and double-integrator (DI) agents with nonidentical unknown control directions by a suitable selection of the distributed nonlinear PI functions. Moreover, as a special case, the proposed algorithms are applied to strongly connected and fixed graphs. Finally, simulation examples are given to show the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

Frequency-domain analysis of dynamic systems is important across many areas of engineering. However, while there are many analysis methods for linear systems, the problem is much less widely studied for nonlinear systems. Frequency-domain analysis of nonlinear systems using frequency response functions (FRFs) is particularly important to reveal resonances, super/subh-armonics, and energy transfer across frequencies. In this paper, the novel contribution is a time-domain, model-based approach to describing the uncertainty of nonlinear systems in the frequency domain. The method takes a nonlinear input–output time-domain model that has normally distributed parameters and propagates that uncertainty into the frequency domain using analytic expressions based on FRFs. We demonstrate the approach on both synthetic examples of nonlinear systems and a real-world nonlinear system identified from experimental data. We benchmark the proposed approach against a brute-force technique based on Monte Carlo sampling and show that there is good agreement between the methods. [ABSTRACT FROM AUTHOR]

Sensors are activated/deactivated according to a sensor activation policy (SAP), which is a decision function whose domain is the language of the system. An SAP is minimal for diagnosability if it is at the point where the system is diagnosable, but any additional deactivation prevents correct system diagnosis. Given that the system is diagnosable when all sensors are always activated, we find in this paper that minimal SAP for diagnosability does not always exist. We therefore develop algorithms to compute a minimal SAP under which the system is pseudodiagnosable. Adhering to such a policy extends the window of opportunity for proper system diagnosis indefinitely, but with the compromise that later policy amendments are allowed. [ABSTRACT FROM AUTHOR]

All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multi-agent systems. Under these assumptions, Olfati-Saber in a recent IEEE TRANSACTIONS ON AUTOMATIC CONTROL paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multi-agent flocking in the absence of the above two assumptions. We first show that, even when only a fraction of agents are informed, the Olfati-Saber flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be influenced by the informed agents from time to time during the evolution. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity. In the situation where the virtual leader travels with a varying velocity, we propose modification to the Olfati-Saber algorithm and show that the resulting algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification of static nonlinear components in a complex interconnected system. These nonlinear components are treated nonparametrically, in the sense that no natural parameterization is assumed to be available. A unified framework based on linear fractional transformations for exploring these identification problems is developed. Two key assumptions are made: the linear components of the interconnection are known, and the inputs to all the nonlinear components are available. Under these assumptions, a novel identification algorithm is offered. This algorithm estimates the nonlinear components by minimizing a quadratic cost function. A critical component of this cost function is the inclusion of a dispersion function that captures the requirement that the estimated nonlinearities be static. It is shown that the estimated nonlinearities converge asymptotically to their "true" values under certain identifiability and persistence of excitation conditions. Computable tests for identifiability and sufficient conditions for persistence of excitation are offered. The results in this paper strongly suggest that the most tractable identification problems for nonlinear interconnected systems are those where the inputs to all the nonlinear blocks are measured. [ABSTRACT FROM AUTHOR]

Arbitrary high precision output tracking is one of the most desirable control objectives found in industrial applications regardless of measurement errors. The main purpose of this paper is to supply to the iterative learning control (ILC) designer guide- lines to select the corresponding learning gain in order to achieve this control objective. For example, if certain conditions are met, then it is necessary for the learning gain to converge to zero in the learning iterative domain. In particular, this paper presents necessary and sufficient conditions for boundedness of trajectories and uniform tracking in presence of measurement noise and a class of random reinitialization errors for a simple ILC algorithm. The system under consideration is a class of discrete-time affine non-linear systems with arbitrary relative degree and arbitrary number of system inputs and outputs. The state function does not need to satisfy a Lipschitz condition. This work also provides a recursive algorithm that generates the appropriate learning gain functions that meet the arbitrary high precision output tracking objective. The resulting tracking output error is shown to converge to zero at a rate inversely proportional to square root of the number of learning iterations in presence of measurement noise and a class of reinitialization errors. Two illustrative numerical examples are presented. [ABSTRACT FROM AUTHOR]

This paper focuses on computational aspects of the realization of nonlinear multi-input multi-output systems. Instead of the algorithmic solutions, provided in earlier works, the explicit formulas are presented, which enable to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The solution is based on the concept of adjoint polynomials and requires a minimal amount of computations. The formulas are implemented in computer algebra system Mathematica and made available online via web Mathematica tools. [ABSTRACT FROM PUBLISHER]

The nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory. The extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated. In this paper, we propose constructive algorithms for decomposing a nonlinear system that is affine in control. These algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs. They lead to various normal form representations and reveal the structure at infinity, the zero dynamics and the invertibility properties, all of which represent nonlinear equivalences of relevant linear system structural properties. [ABSTRACT FROM AUTHOR]

Abstract-The use of a neural network (NN) as a feedforward control element to compensate for nonlinear system uncertainties has been investigated for over a decade. Typical NN-based controllers yield uniformly ultimately bounded (UUB) stability results due to residual functional reconstruction inaccuracies and an inability to compensate for some system disturbances. Several researchers have proposed discontinuous feedback controllers (e.g., variable structure or sliding mode controllers) to reject the residual errors and yield asymptotic results. The research in this paper describes how a recently developed continuous robust integral of the sign of the error (RISE) feedback term can be incorporated with a NN-based feedforward term to achieve semi-global asymptotic tracking. To achieve this result, the typical stability analysis for the RISE method is modified to enable the incorporation of the NN-based feedforward terms, and a projection algorithm is developed to guarantee bounded NN weight estimates. [ABSTRACT FROM AUTHOR]

In this paper, a continuous feedback tracking controller is developed for a class of high-order multi-input multi-output (MIMO) nonlinear systems with an input gain matrix that has nonzero leading principal minors but can be nonsymmetric. Under the mild assumption that the signs of the leading minors of the control input gain matrix are known, the controller yields locally uniformly ultimately bounded (UUB) tracking while compensating for unstructured uncertainty in both the drift vector and the input matrix. First, a full-state feedback controller is designed based on limited assumptions on the structure of the system nonlinearities, and the singularity-free controller is proven to yield locally UUB tracking through a Lyapunov-based analysis. Then, it is shown that an output feedback control can be designed based on a high-gain observer. Simulation results are provided to illustrate the performance of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the state estimation problem for stochastic nonlinear differential systems, driven by standard Wiener processes, and presents a filter that is a generalization of the classical Extended Kalman-Bucy filter (EKBF). While the EKBF is designed on the basis of a first order approximation of the system around the current estimate, the proposed filter exploits a Carleman-like approximation of a chosen degree v ≥ 1. The approximation procedure, applied to both the state and the measurement equations, allows to define an approximate representation of the system by means of a bilinear system, for which a filtering algorithm is available from the literature. Numerical simulations on an example show the improvement, in terms of sample error covariance, of the filter based on the first-order, second-order and third-order system approximations (v = 1,2,3). [ABSTRACT FROM AUTHOR]

A systematic approach to the chattering analysis in systems with second-order sliding modes is developed. The neglected actuator dynamics is considered to be the main cause of chattering in real systems. The magnitude of oscillations in nonlinear systems with unmodeled fast nonlinear actuators driven by second-order sliding-mode control generalized suboptimal (2-SMC G-SO) algorithms is evaluated. Sufficient conditions for the existence of orbitally stable periodic motions are found in terms of the properties of corresponding Poincaré maps. For linear systems driven by 2-SMC G-SO algorithms, analysis tools based on the frequency-domain methods are developed. The first of these techniques is based on the describing function method and provides for a simple approximate approach to evaluate the frequency and the amplitude of possible periodic motions. The second technique represents a modified Tsypkin's method and provides for a relatively simple, theoretically exact, approach to evaluate the periodic motion parameters. Examples of analysis and simulation results are given throughout this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present robust stability results for constrained discrete-time nonlinear systems using a finite-horizon model predictive control (MPC) algorithm for which we do not require the terminal cost to have any particular properties. We introduce a definition that attempts to characterize the robustness properties of the MPC optimization problem. We assume the systems under consideration satisfy this definition (for which we give sufficient conditions) and make two further assumptions. These are that the value function is bounded by a K∞ function of a state measure (related to the distance from the state to some target set) and that this measure is detectable from the stage cost used in the MPC algorithm. We show that these assumptions lead to stability that is robust to sufficiently small disturbances. While in general the results are semiglobal and practical, when the detectability and upper bound assumptions are satisfied with linear K∞ functions, the stability and robustness are either semiglobal or global (with respect to the feasible set). We discuss algorithms employing terminal inequality constraints and also provide a specific example of an algorithm that employs a terminal equality constraint. [ABSTRACT FROM AUTHOR]

Most verification techniques for highly populated discrete systems suffer from the state explosion problem. The ‘fluidification’ of discrete systems is a classical relaxation technique that aims to avoid the state explosion problem. Continuous Petri nets are the result of fluidifying traditional discrete Petri nets. In continuous Petri nets the firing of a transition is not constrained to the naturals but to the non-negative reals. Unfortunately, some important properties, as liveness, may not be preserved when the discrete net model is fluidified. Therefore, a thorough study of the properties of continuous Petri nets is required. This paper focuses on the study of deadlock-freeness in the framework of mono-T-semiflow continuous Petri nets, i.e., conservative nets with a single repetitive sequence (T-semiflow). The study is developed both on untimed and timed systems. Topological necessary conditions are extracted for this property. Moreover, a bridge relating deadlock-freeness conditions for untimed and timed systems is established. [ABSTRACT FROM AUTHOR]

We present a nonsmooth output feedback framework for local and/or global stabilization of a class of nonlinear systems that are not smoothly stabilizable nor uniformly observable. A systematic design method is presented for the construction of stabilizing, dynamic output compensators that are nonsmooth but Hölder continuous. A new ingredient of the proposed output feedback control scheme is the introduction of a recursive observer design algorithm, making it possible to construct a reduced-order observer step-by-step, in a naturally augmented manner. Such a nonsmooth design leads to a number of new results on output feedback stabilization of nonlinear systems. One of them is the global stabilizability of a chain of odd power integrators by Hölder continuous output feedback. The other one is the local stabilization using nonsmooth output feedback for a wide class of nonlinear systems in the Hessenberg form studied in a previous paper, where global stabilizability by nonsmooth state feedback was already proved to be possible. [ABSTRACT FROM AUTHOR]

It is well known that a nonlinear optimal control requires the solution to a two-point boundary value problem or to a nonlinear partial differential equation and that such a solution can only be obtained off line by numerical iteration. In this paper, a new and near-optimal control design framework is proposed for controlling any nonholonomic system in the chained form. The proposed design is based upon thorough study of uniform complete controllability of the corresponding linear time varying nominal System. It is shown that, no matter whether the first component u1d(t) of reference input vector is uniformly nonvanishing or simply nonconvergent to zero or vanishing or identically zero, uniform complete controllability of the (nominal) system can be recovered by employing the proposed time-folding/unfolding technique. Upon establishing the common property of uniform complete controllability, the proposed framework can be used to design both trajectory tracking control and regulation control in a systematic and unified manner. Using duality, uniform complete observability can also be established, a closed-form and exponentially convergent observer can be synthesized, and the controls designed using the proposed framework can be either state-feedback or output-feedback. The tracking controls are designed using the same three-step process. That is, design of the proposed controls starts with optimal control solutions to two linear nominal subsystems, one time-invariant and the other time varying. The two solutions combined together render a globally stabilizing suboptimal control for the overall system. Then, the optimality condition is invoked to determine the distance between the suboptimal control and the optimal one. Consequently, an improved control can be obtained by introducing a nonlinear additive control term in such a way that the distance aforementioned is minimized as much as possible in closed form. An example is used to show that regulation control can be designed similarly. All the controls designed are in simple closed forms and hence real-time implementable, they are time varying and smooth, globally and exponentially/asymptotically stabilizing, and they are near optimal since their closeness to the optimal control (attainable only offline) can be measured, monitored on line, and has been minimized. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a framework for the design of sliding-mode based controllers for multi-input affine nonlinear systems. In this framework the control effort goes to zero as the state approaches the sliding surface, a key feature for practical implementation. The sliding surface is a submanifold with codimension equal to the dimension of the involutive distribution ɡ generated by the controlled vector fields rather than the dimension of their linear span. We also allow nonzero vectors in ɡ to be tangent to the sliding surface, the singular case in sliding-mode control. [ABSTRACT FROM AUTHOR]

In this paper, we consider the design of globally asymptotically stabilizing state-dependent switching rules for multimodal systems, first restricting attention to linear time-in-variant (LTI) systems with only two states for the switch, and then generalizing the results to multimodal LTI systems and to nonlinear systems. In all cases, the systems considered do not allow the construction of a single quadratic Lyapunov function and, hence, fall in the class of problems that require multiple Lyapunov functions and thus are nonconvex. To address the challenge of nonconvexity, we introduce probabilistic algorithms, and prove their probability-one convergence under a new notion of convergence. Then, to reduce complexity, we develop modified versions of the algorithm. We also present a class of more general nonconvex problems to which this approach can be applied. The results are illustrated using two- and three-dimensional systems with multiple switch states. [ABSTRACT FROM AUTHOR]

The convergence of the iterative identification algorithm for the Hammerstein system has been an open problem for a long time. In this paper, a detailed study is carried out and various convergence properties of the iterative algorithm are derived. It is shown that the iterative algorithm with normalization is convergent in general. Moreover, it is shown that convergence takes place in one step (two least squares iterations) for finite-impulse response Hammerstein models with Ltd. inputs. [ABSTRACT FROM AUTHOR]

In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, In the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the "disturbance-like" term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance. [ABSTRACT FROM AUTHOR]