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We consider exact system identification in the behavioral setting: Given an exact (noise-free) finite time series, find the set of bounded complexity linear time-invariant systems that fit the data exactly. First, we modify the notion of the most powerful unfalsified model for the case of finite data by fixing the number of inputs and minimizing the order. Then, we give necessary and sufficient identifiability conditions, i.e., conditions under which the true data generating system coincides with the most powerful unfalsified model. Finally, we show that the set of bounded complexity exact models is affine: Every exact model is a sum of the most powerful unfalsified model and an autonomous model with bounded complexity. [ABSTRACT FROM AUTHOR]

In this article, the problem of simultaneous leader–following consensus and parameter estimation is studied for a class of multiagent systems subject to an uncertain leader system. The leader system is described by a sum of sinusoids with unknown amplitudes, frequencies, and phases. A fully distributed adaptive observer is established for each agent to estimate the unknown frequencies of the leader without using any global information. It is shown that if the signal of the leader is sufficiently rich, the estimation errors of the unknown frequencies converge to zero asymptotically for all the agents. Based on the designed distributed adaptive observer, a distributed adaptive control law is synthesized for each agent to solve the leader–following consensus problem. [ABSTRACT FROM AUTHOR]

This article addresses the problem of robust stabilization of uncertain linear systems by static state- and output-feedback control laws. The uncertainty is supposed to belong to a polytope and both continuous- and discrete-time systems are investigated. Contrarily to the main stream of the linear matrix inequality (LMI)-based robust stabilization methods available in the literature, where the product between the Lyapunov (or slack variable) and control gain matrices is transformed in a new variable, this article proposes a change of paradigm, avoiding the standard change of variables and providing synthesis conditions that deal directly with the control gain as an optimization variable. The design procedure is formulated in terms of a locally convergent iterative algorithm based on LMIs, having as main novelties the following points: Both the Lyapunov and the closed-loop dynamic matrices appear affinely in the conditions; the iterative scheme involves the slack variables only, avoiding the classic alternation between the Lyapunov matrix and the control gain; an extra degree of freedom is created in terms of an additional scalar variable, which also appears affinely in the conditions and represents a scaling on the closed-loop dynamic matrix; a smart termination for the algorithm through a stability analysis condition. Numerical experiments based on exhaustive simulations show that all these features combined provide a robust stabilization technique capable to outperform the best available methods in the literature in terms of effectiveness, being specially suitable to address static output-feedback and decentralized control problems. [ABSTRACT FROM AUTHOR]

The problem of output tracking is addressed in this article by a reformulation in terms of a two-point boundary value problem for the plant's zero dynamics, which is allowed to be unstable. On this basis, a hybrid feedback regulator ensuring output tracking is then designed. The robustness properties of the proposed regulator as well as connections with periodic (cheap) optimal control, output regulation, and possible extensions to the nonlinear setting are also discussed. [ABSTRACT FROM AUTHOR]

Relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi-input multi-output nonlinear plant and an integral controller. Roughly speaking, it is shown that if the composition of the plant equilibrium input–output map and the integral feedback gain is infinitesimally contracting, then the closed-loop system is exponentially stable if the integral gain is sufficiently low. The main result is illustrated with an application arising in frequency control of ac power systems. We demonstrate how the contraction condition can be checked computationally via semidefinite programming, and how integral gain matrices can be synthesized via convex optimization to achieve robust L2 performance in the presence of nonlinearity and uncertainty. [ABSTRACT FROM AUTHOR]

We investigate discrete-time closed-loop dynamics consisting of a linear plant, a linear controller, and a wireless network that connects the sensors and the actuators to the control unit. The objective, as well as the main contribution of this article, is the static output feedback control synthesis under given network specifications. Precisely, network features are formulated in terms of stochastic allowable transmission interval (SATI), which is a concept well suited for the time-triggered control of wireless network control systems (WNCS). Given SATI parameters, we provide sufficient conditions in terms of linear matrix inequalities, under which we can design a static output feedback controller that stabilizes the closed-loop WNCS in mean square sense. Moreover, we guarantee that a quadratic control cost is less than a given bound. Consequently, the results can be used to ensure not only stability but also desired control performances for the WNCS and its SATI characteristics. [ABSTRACT FROM AUTHOR]

This article presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class of problems where the cost is expressed as a time-varying norm-like function of the control input, enabling inclusion of complex operational constraints in the control planning problem. First, it is shown that the reachable sets for this problem have identical properties to those in prior works using constant cost functions, enabling use of existing algorithms in conjunction with newly derived contact and support functions. By reformulating the optimal control problem as a semi-infinite convex program, it is also demonstrated that the semi-infinite component of the commonly studied primer vector is an outward normal vector to the reachable set at the target state. Using this formulation, a fast and robust algorithm that provides globally optimal impulsive control input sequences is proposed. The algorithm iteratively refines estimates of an outward normal vector to the reachable set at the target state and a minimal set of control input times until the optimality criteria are satisfied to within a user-specified tolerance. Next, optimal control inputs are computed by solving a quadratic program. The algorithm is validated through simulations of challenging example problems based on the recently proposed miniaturized distributed occulter/telescope small satellite mission, which demonstrate that the proposed algorithm converges several times faster than comparable algorithms in the literature. [ABSTRACT FROM AUTHOR]

We study adaptive fault-tolerant tracking control for uncertain linear systems. Based on recent results in funnel control, and the time-varying Byrnes–Isidori form, we develop a low-complexity model-free controller that achieves prescribed performance of the tracking error for any given sufficiently smooth reference signal. Within the considered system class, we allow for more inputs than outputs as long as a certain redundancy of the actuators is satisfied. An important role in the controller design is played by the controller weight matrix. This is a rectangular input transformation chosen such that in the resulting system, the zero dynamics, which are assumed to be uniformly exponentially stable, are independent of the new input. We illustrate the fault-tolerant funnel controller by an example of a linearized model for the lateral motion of a Boeing 737 aircraft. [ABSTRACT FROM AUTHOR]

This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transmission. In the set-up adopted, sensors and actuators communicate through a network with a strongly connected topology. Unlike the case of centralized linear systems, for which the separation principle holds, the above practical assumption prevents the separate design of observers, and controller because each of the nodes does not necessarily have access to the control inputs generated at all the other nodes. We derive a linear distributed Luenberger observer, and a set of sufficient conditions that guarantee ultimate boundedness of the estimation error, and system state vectors, with bounds that depend on the $\mathcal {L}_{\infty }$ norm of the noise signals, and the number of bits used in the transmissions. A numerical example illustrates the performance and effectiveness of the proposed algorithm in controlling a network of open-loop unstable systems. [ABSTRACT FROM AUTHOR]

In this article, we propose two new iterative algorithms to solve the frequency-limited Riemannian optimization model order reduction problems of linear and bilinear systems. Different from the existing Riemannian optimization methods, we design a new Riemannian conjugate gradient scheme based on the Riemannian geometry notions on a product manifold, and then generate a new search direction. Theoretical analysis shows that the resulting search direction is always descent with depending neither on the line search used, nor on the convexity of the cost function. The proposed algorithms are also suitable for generating reduced systems over a frequency interval in bandpass form. Finally, two numerical examples are simulated to demonstrate the efficiency of our algorithms. [ABSTRACT FROM AUTHOR]

This article studies unknown input observer design for linear parameter-varying systems in a bounded error context. By presenting a novel unknown input observer structure, the output equation of linear parameter-varying systems is not restricted to be in a linear form. Moreover, by integrating decoupling technique and set-membership approach, a compromise is achieved between the restrictiveness and the conservativeness of estimation. Based on P-radius criteria, sufficient design conditions are derived in terms of linear matrix inequalities. Finally, numerical simulations of a vehicle lateral dynamics system are conducted to demonstrate the validity of the presented method. [ABSTRACT FROM AUTHOR]

This article studies the constrained switching (linear) system which is a discrete-time switched linear system whose switching sequences are constrained by a deterministic finite automaton. The stability of a constrained switching system is characterized by its constrained joint spectral radius that is known to be difficult to compute or approximate. Using the semitensor product of matrices, the matrix-form expression of a constrained switching system is shown to be equivalent to that of a lifted arbitrary switching system. Then, the constrained joint/generalized spectral radius of a constrained switching system is proven to be equal to the joint/generalized spectral radius of its lifted arbitrary switching system which can be approximated by off-the-shelf algorithms. [ABSTRACT FROM AUTHOR]

In the article, we study the distributed model predictive control (DMPC) problem for a network of linear discrete-time systems, where the system dynamics are decoupled, the system constraints are coupled, and the communication networks are described by time-varying directed graphs. A novel distributed optimization algorithm called the push-sum dual gradient (PSDG) algorithm is proposed to solve the dual problem of the DMPC optimization problem in a fully distributed way. We prove that the sequences of the primal, and dual variables converge to their optimal values. Furthermore, to solve the implementation issues, stopping criteria are designed to allow early termination of the PSDG Algorithm, and the gossip-based push-sum algorithm is proposed to check the stopping criteria in a distributed manner. It is shown that the optimization problem is iteratively feasible, and the closed-loop system is exponentially stable. Finally, the effectiveness of the proposed DMPC approach is verified via an example. [ABSTRACT FROM AUTHOR]

This article is about a real-time model predictive control algorithm for large-scale, structured linear systems with polytopic control constraints. The proposed controller receives the current state measurement as an input, and computes a suboptimal control reaction by evaluating a finite number of piecewise affine functions that correspond to the explicit solution maps of small-scale parametric quadratic programming (QP) problems. We provide asymptotic stability guarantees, which can be verified offline. The feedback controller is computing approximations of the optimal input, because we are enforcing real-time requirements assuming that it is not possible to solve the given large-scale QP in the given amount of time. Here, a key contribution of this article is that we provide a bound on the suboptimality of the controller. The approach is illustrated by benchmark case studies. [ABSTRACT FROM AUTHOR]

Design of output feedback controllers applied to the regulation problem for constrained linear discrete-time systems via set-invariance techniques is studied. Output feedback controlled-invariant (OFCI) polyhedra are used to ensure that state and input constraints are satisfied even in the presence of additive disturbances and measurement noise. Necessary and sufficient conditions for a polyhedral set to be OFCI are presented. A dynamic output feedback compensator is proposed through the construction of an OFCI set for an augmented system. Based on the measured output and on the compensator state, which constitutes an estimate of the system state, a suitable control sequence is computed via linear programming to enforce the constraints. The uncertainty on the state is progressively reduced using the contraction of an invariant set associated to the estimator. With our approach, as illustrated through numerical examples, by embedding the estimator in the compensator structure and using the OFCI concept, it is possible to obtain solutions with larger sets of admissible initial states and admissible initial estimation errors, compared to approaches available in the literature. [ABSTRACT FROM AUTHOR]

In this article, we investigate controllability of hybrid systems. We use hybrid machines to model such hybrid systems. The model consists of an automaton and a linear time-invariant system. The control goal is to drive the continuous state from any initial state to any final state. To achieve this goal, controls at both the discrete-event level and the continuous-variable level are used. Control at the discrete-event level can force some forcible events, and disable some controllable events. For the case that all events are controllable and forcible, and the graph of the automaton is strongly connected, a necessary and sufficient condition for controllability is obtained, using some existing results on controllability of switched linear systems. For three other cases, sufficient conditions are derived. If a hybrid system is not controllable, we design a supervisor to control the discrete-event part to ensure that the system becomes controllable after some finite transitions if possible. We find a necessary and sufficient condition for such a discrete-event control to exist. [ABSTRACT FROM AUTHOR]

We consider the problem of steering a linear stochastic system between two endpoint degenerate Gaussian distributions in finite time. This accounts for those situations in which some but not all of the state entries are uncertain at the initial, $t=0$ , and final time, $t=T$. This problem entails nontrivial technical challenges, as the singularity of terminal state covariance causes the control to grow unbounded at the final time $T$. Consequently, the entropic interpolation (Schrödinger bridge) is provided by a diffusion process, which is not finite energy, thereby placing this case outside of most of the current theory. In this article, we show that a feasible interpolation can be derived as a limiting case of earlier results for nondegenerate cases, and that it can be expressed in closed form. Moreover, we show that such interpolation belongs to the same reciprocal class of the uncontrolled evolution. By doing so, we also highlight a time symmetry of the problem, contrasting dual formulations in the forward and reverse time directions, where in each, the control grows unbounded as time approaches the endpoint (in the forward and reverse time direction, respectively). [ABSTRACT FROM AUTHOR]

Network inference has been attracting increasing attention in several fields, notably systems biology and biomedicine. Indeed, one of our biggest challenges is to uncover and understand complex molecular networks behind cells and organisms. A network is mainly characterized by its topology and internal dynamics. In particular, sparse topologies with stable dynamics are properties present in most real-world networks. Moreover, experiments typically measure a partial set of nodes. Linear systems have been used as approximations of complex nonlinear systems in a wide range of applications. Although they exhibit simpler dynamics, they can easily model unmeasured nodes, e.g., via transfer functions, which is not possible for nonlinear systems. This article explores these properties and considers general linear network models. It develops a method, based on reversible jump Markov chain Monte Carlo, to estimate the confidence of all links and produce the most likely topology. Monte Carlo simulations indicate that our approach consistently produces more accurate networks compared with other state-of-the-art methods, including kernel-based methods, nonlinear ordinary-differential-equation-based methods (iCheMA), and machine-learning-based methods (dynGINIE3). We show that this is also true on a well-known biological nonlinear model. The proposed method can be used in a wide range of applications, such as systems biology and biomedicine, and fault detection and diagnosis. [ABSTRACT FROM AUTHOR]

In this article, positivity and global exponential stability for a class of timescale-type differential-difference equations with bounded time-varying delay are considered. At first, a sufficient and necessary condition for the positivity of matrix-valued timescale-type exponential function is obtained. Based on this, an explicit criterion for the positivity of coupled timescale-type differential-difference equations with delays bounded above is acquired by timescale-type induction method. Besides, a sufficient and necessary condition of its positivity is obtained when the delay is both bounded above and below by two positive reals. Then, a concise criterion that guarantees the global exponential stability of the considered system is derived based upon analytical techniques of time scales and positivity constraint. On top of that, the theoretical results are applied to investigate the positivity and stability for a class of timescale-type neutral linear systems with bounded time-varying delays. Two numerical examples are given to illustrate the validity of the results. [ABSTRACT FROM AUTHOR]

This article develops a robust linear quadratic regulator (LQR) approach applicable to nonhomogeneous Markov jump linear systems with uncertain transition probability distributions. The stochastic control problem is investigated under two equivalent formulations, using i) minimax optimization theory, and ii) a total variation distance metric as a tool for codifying the level of uncertainty of the jump process. By following a dynamic programming approach, a robust optimal controller is derived, which in addition to minimizing the quadratic cost, it also restricts the influence of uncertainty. A solution procedure for the LQR problem is also proposed, and an illustrative example is presented. Numerical results indicate the applicability and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article studies the performance evaluation of distributed linear regression Kalman filtering fusion for nonlinear systems. Sufficient conditions are established for the convergence of the centralized fusion (CF) under the assumption of bounded estimation error covariance, and a measure of performance is derived from the convergence conditions. By the performance analysis, it can be found that the CF has a better performance than the distributed fusion with feedback, especially at the beginning of the estimation. Moreover, the performance of the local estimator can be improved by receiving the fused estimate from the fusion center, which is different from the fusion estimation in linear systems. Finally, by simulations of a target tacking example, the comparisons of the centralized fusion and the distributed fusion with and without feedback are presented to show the accuracy of the performance analysis. [ABSTRACT FROM AUTHOR]

This article considers the problem of output feedback funnel control for a class of uncertain nonlinear systems with arbitrary known relative degree. By utilizing the funnel control approach with a barrier Lyapunov function, a novel adaptive output feedback controller is constructed recursively, which accomplishes the output tracking with prescribed transient behavior. The developed control scheme features that the precise knowledge of system nonlinearities, including generally required bounding functions, is not needed. A physical example is performed to verify the effectiveness of the proposed theoretical findings. [ABSTRACT FROM AUTHOR]

In this article, we deal with the study of the determinantal assignment problem (DAP) when the parameters of the compensator are not entirely free, but some of them are fixed. The problem is reduced to a restricted form of an exterior algebra problem (decomposability of multivectors), which is referred to as partial decomposability problem. We study this problem and in case that this problem has no solution, we examine the problem of approximate partial decomposability. We treat the problem of exact or partial decomposability into a vector and a multivector of lower dimension. If this procedure is repeated then this results in an approximation of the initial multivector into a decomposable vector. The approximation of a vector by an optimal decomposable multivector is a nonlinear procedure and has been solved completely using the power method. The method developed in this article, although it produces a suboptimal solution, can be used alternatively for the solution of DAP or the approximate DAP, as a shorter and easier approach, because it is based on known tools as the singular value decomposition. We apply these results to treat the restricted approximate decomposability problem, which leads to approximate solutions to the pole placement and zero assignment problems. [ABSTRACT FROM AUTHOR]

This article deals with the problem of formulating an adaptive model-predictive control strategy for constrained uncertain systems. We consider a linear system in the presence of bounded time-varying additive uncertainty. The uncertainty is decoupled as the sum of a process noise with known bounds and a time-varying offset that we wish to identify. The time-varying offset uncertainty is assumed unknown pointwise in time. Its domain, called the feasible parameter set, and its maximum rate of change are known to the control designer. As new data become available, we refine the feasible parameter set with a set-membership-method-based approach, using the known bounds on process noise. We consider the case of probabilistic constraints on system states, with hard constraints on actuator inputs. We robustly satisfy the imposed constraints for all possible values of the offset uncertainty in the feasible parameter set. By imposing adequate terminal conditions, we prove recursive feasibility and stability of the proposed algorithm. The efficacy of the proposed approach is illustrated with a detailed numerical example. [ABSTRACT FROM AUTHOR]

This article is concerned with the sliding mode control (SMC) for stabilizing a switched linear system with external disturbances and uncertain nonlinearities. The state sampling is implemented by an event-triggered mechanism (ETM) and the sampled data are transmitted through a limited-bandwidth digital channel. The main challenge of such a work comes from the quantizer saturation and quantization error in the SMC design with finite-level quantization and the mismatched control caused by the switch and event-triggered sampling. To solve the above problem, we at first present an ETM and a limited-information-based SMC law. Then, a new discrete-time level-sets method is proposed to develop the dynamic quantization policy (DQP). If the disturbance bound is known, the DQP can avoid the quantizer saturation without the need of online detection. A switching law and quantization parameter conditions are provided to ensure the convergence of the state trajectory. At last, the result is generalized to the unknown bound of disturbance. The limited-information control problem of a single-link manipulator is taken as a potential application of the proposed method. [ABSTRACT FROM AUTHOR]

We characterize a class of systems for which the H-infinity optimal control problem can be simplified in a way that enables sparse solutions and efficient computation. For a subclass of the systems, an optimal controller can be explicitly expressed in terms of the matrices of the system's state-space representation. In many applications, the controller given by this formula, which is static, can be implemented in a decentralized or distributed fashion. Examples are temperature dynamics in buildings, water irrigation, and electrical networks. [ABSTRACT FROM AUTHOR]

The purpose of this article is to reduce some technical difficulties related to the complexity of stability and feasibility analysis of Model Predictive Control (MPC) as well as to reduce the complexity of the relative optimization procedure. The new approach is based on a two degrees of freedom control scheme where the output r(k) of a feedforward input estimator is used as input forcing the closed-loop system Σƒ. This latter is given by the feedback connection of a Linear Time Invariant (LTI) plant with a dynamic output controller. The task of the controller is to guarantee the stability of Σƒ, as well as the fulfillment of hard constraints for any r(k) satisfying an “a priori” determined admissibility condition. The input r(k) is computed through the online minimization of a quadratic cost functional and is applied to Σƒ according to the usual MPC strategy. To simplify the constrained optimization problem, the input r(k) forcing Σƒ is assumed to be given by a B-spline function. This greatly decreases the number of decision variables of the online optimization procedure because B-splines are universal approximators which admit a parsimonious parametric representation. Moreover such parameterization allows us to reformulate the minimization of the cost functional as a box Constrained Least Squares (CLS) problem. It is shown that stability and recursive feasibility of the adopted MPC strategy are guaranteed in advance, regardless the chosen prediction horizon. [ABSTRACT FROM AUTHOR]

In hybrid model predictive control (MPC), a mixed-integer quadratic program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC, we expect consecutive problem instances to be nearly identical. This article addresses the question of how computations performed at one time step can be reused to accelerate (warm start) the solution of subsequent MIQPs. Reoptimization is not a rare practice in integer programming: for small variations of certain problem data, the branch-and-bound algorithm allows an efficient reuse of its search tree and the dual bounds of its leaf nodes. In this article, we extend these ideas to the receding-horizon settings of MPC. The warm-start algorithm we propose copes naturally with arbitrary model errors, has a negligible computational cost, and frequently enables an a priori pruning of most of the search space. Theoretical considerations and experimental evidence show that the proposed method tends to reduce the combinatorial complexity of the hybrid MPC problem to that of a one-step look-ahead optimization, greatly easing the online computation burden. [ABSTRACT FROM AUTHOR]

This article proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalized diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on local information exchange between neighboring nodes, local computation, and local storage. For an acyclic graph under the condition of diagonal dominance, the algorithm is shown to converge to the correct solution in a finite number of iterations, equaling the graph diameter. For a loopy graph, the algorithm is shown to converge to the correct solution asymptotically. Simulations verify that the proposed algorithm significantly outperforms the classical Jacobi method and an orthogonal projection-based method. [ABSTRACT FROM AUTHOR]

In this article, we study the robust output regulation problem of linear systems by an event-triggered output feedback control law. We first summarize the solvability of the linear robust output regulation problem by the internal model design. Then, we implement this continuous-time control law by an event-triggered output feedback control law together with an output-based triggering mechanism. We show that, under almost the same solvability conditions as those for the linear robust output regulation problem, the robust output regulation problem can also be solved by an event-triggered output feedback control law without incurring Zeno phenomenon. Furthermore, we show that, it is possible to solve the robust output regulation problem practically while preventing the interevent time from approaching zero as time tends to infinity. [ABSTRACT FROM AUTHOR]

In this article, uncertain continuous-time and discrete-time linear time-invariant systems are considered. The uncertainties are assumed to affect polynomially the dynamics of the system and they can be structured. The problem of computing the distance to internal instability of an internally exponentially stable nominal system is solved by using tools from algebraic geometry, thus extending previous results valid in case of unstructured uncertainties. The choice of the nominal system is formulated and solved as the choice of a point in the parameter space that is sufficiently far from the boundary of the domain of stability. A simple example of application to robust control is outlined. [ABSTRACT FROM AUTHOR]

In this article, we face the problem of detecting setpoint attacks in networked control systems. We consider a setup where the reference signal (also known as setpoint) is generated by a control center remotely located with respect to a standard feedback controller. In this scenario, an attacker with sufficient resources can exploit the communication channel to alter the setpoint signal and ultimately affect the tracking performance of the control system. With respect to this problem, we propose a novel distributed control architecture that, taking advantage of peculiar capabilities of the command governor control paradigm, enables the detection of reference attacks. We formally prove that for constrained linear systems such detector exists. Moreover, by limiting the attacker's disclosure resources with superimposed cryptographically secure pseudorandom signals, we show that the absence of advanced stealthy attacks is also ensured. Finally, a solid numerical simulation investigating setpoint attacks on the flight control system of a single-engine fighter is presented to provide tangible evidence of the features of the presented methodology. [ABSTRACT FROM AUTHOR]

This article investigates the stability of continuous-time switched linear systems with dwell-time constraints. A fresh insight into this established problem is provided via novel stability conditions that require the solution to a family of differential Lyapunov equations and algebraic Lyapunov equations. The proposed analysis, which leads to a peculiar Lyapunov function that is decreasing in between and at switching instants, enjoys the following properties: it achieves the same dwell time as the well-known result in the research “stability and stabilization of continuous time switched linear systems” by Geromel and Colaneri; it removes the increasing computational complexity of the linear interpolation method; it leads to a straightforward counterpart for discrete-time switched linear systems.We show the application of this methodology to the problem of adaptive control of switched linear systems with parametric uncertainties. [ABSTRACT FROM AUTHOR]

We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include the following, first, a unified treatment of the continuous and the discrete-time cases; second, the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and, third, an alternative estimator ensuring convergence in finite-time whose adaptation gain, in contrast with the existing one, does not converge to zero. Simulations that illustrate our results are also presented. [ABSTRACT FROM AUTHOR]

In this article, we investigate the problem of actuator selection for linear dynamical systems. We develop a framework to design a sparse actuator schedule for a given large-scale linear system with guaranteed performance bounds using deterministic polynomial-time and randomized approximately linear-time algorithms. First, we introduce systemic controllability metrics for linear dynamical systems that are monotone and homogeneous with respect to the controllability Gramian. We show that several popular and widely used optimization criteria in the literature belong to this class of controllability metrics. Our main result is to provide a polynomial-time actuator schedule that on average selects only a constant number of actuators at each time step, independent of the dimension, to furnish a guaranteed approximation of the controllability metrics in comparison to when all actuators are in use. Our results naturally apply to the dual problem of sensor selection, in which we provide a guaranteed approximation to the observability Gramian. We illustrate the effectiveness of our theoretical findings via several numerical simulations using benchmark examples. [ABSTRACT FROM AUTHOR]

Conditions for robust input–output stability of barrier-based model predictive control of linear systems with linear and convex nonlinear (hard or soft) constraints are established through the construction of integral quadratic constraints (IQCs). The IQCs can be used to determine sufficient conditions for global closed-loop stability. In particular, conditions for robust stability can be obtained in the presence of unstructured model uncertainty. IQCs with both static and dynamic multipliers are developed and appropriate convex searches for the multipliers are presented. The effectiveness of the robust stability analysis is demonstrated through an illustrative numerical example. [ABSTRACT FROM AUTHOR]

We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does not require any prior identification step, but only an initially measured input–output trajectory as well as an upper bound on the order of the unknown system. First, we prove exponential stability of a nominal data-driven MPC scheme with terminal equality constraints in the case of no measurement noise. For bounded additive output measurement noise, we propose a robust modification of the scheme, including a slack variable with regularization in the cost. We prove that the application of this robust MPC scheme in a multistep fashion leads to practical exponential stability of the closed loop w.r.t. the noise level. The presented results provide the first (theoretical) analysis of closed-loop properties, resulting from a simple, purely data-driven MPC scheme. [ABSTRACT FROM AUTHOR]

A challenging task in network synchronization is steering the network toward a coherent solution, when the dynamics of the constituent systems are heterogeneous and uncertain. In this situation, synchronization can be achieved via adaptive protocols (with adaptive feedback gains or adaptive coupling gains, or both). However, as state-of-the-art synchronization methods adopt a distributed observer architecture, they require to communicate extra observer variables among neighbors, in addition to the neighbors’ states (or outputs). The distinguishing feature of this article is to show that for heterogeneous and uncertain networks of some classes of linear systems, synchronization is possible without the need for any distributed observer. Such classes are in line with those in model reference adaptive control literature. Lyapunov analysis is used to derive a new adaptive synchronization protocol with the simplest communication architecture, in which both feedback and coupling gains are adapted without any extra communication other than neighbors’ states (in the full-state information case) or neighbors’ outputs (in the partial-state information case). [ABSTRACT FROM AUTHOR]

This article systematically studies consensus of linear multiagent systems (MASs) on directed graphs through adaptive event-triggered control. It presents innovative adaptive event-triggered state-feedback protocols with novel composite event-triggering conditions. Two specific designs in terms of different event-triggering conditions and laws of adaption are first discussed for linear MASs on strongly connected directed graphs, which are then extended to general directed graphs that contain a spanning tree. Moreover, another adaptive event-triggered protocol is proposed for solving leader–follower consensus that tracks a leader of a bounded control input. The protocols inherit the merits of both adaptive control and event-triggered control: the protocols can be implemented in a fully distributed way, since the Laplacian is avoided in design, and each agent only needs to know the relative information between neighbors at discrete instants determined by event-triggering conditions. Compared with the existing related results, the proposed protocols are applicable for linear MASs on general directed graphs, and moreover, the time-dependent term in the event-triggering conditions is allowed to be a class of positive L1 functions. Two numerical examples clearly verify the effectiveness of the proposed protocols. [ABSTRACT FROM AUTHOR]

Max-plus linear (MPL) systems are often described by a transition function, which models the state evolution of the system, and a measurement function, which binds the measures with the system states. Methods for computing the inverse image of a point w.r.t. the measurement function are particularly interesting in applications where it is desirable to obtain information about the system states based on the output observations. The inverse image of a set w.r.t. a nondeterministic MPL system, called uncertain MPL (uMPL) system, can be computed by using the difference-bound matrices (DBM) approach. In this article, we aim to use an interval analysis to propose a method to compute the inverse image of a point w.r.t. an uMPL system. The algorithm proposed has a lower worst-case complexity compared with the DBM approach as previously proposed in the literature. [ABSTRACT FROM AUTHOR]

In this article, we first establish an exponential stability result for a class of linear switched systems and then apply this result to show the existence of the distributed observer for a discrete-time leader system over jointly connected switching networks. Then, we further develop the adaptive distributed observer for the discrete-time leader system over jointly connected switching networks, which has the advantage over the distributed observer in that, it does not require that every follower subsystem know the system matrix of the leader system. As an application of the discrete-time distributed observer, we solve the cooperative output regulation problem of a discrete-time linear multiagent system over jointly connected switching networks. A leader-following formation problem of mobile robots is used to illustrate our design. [ABSTRACT FROM AUTHOR]

The stability of two-dimensional (2-D) linear systems, continuous, discrete, and mixed (hybrid) cases with real or complex coefficients, is considered in this article using a single formalism. Algebraic necessary and sufficient conditions for testing the stability of these systems are developed. The conditions are based on the characteristic polynomial to be void of zero in the stability region which depends on the case being considered. These conditions consist of the stability test of few real univariate polynomials and a real generalized eigenvalue problem. The resulting stability test requires reduced computational complexity compared to existing techniques. A numerical example is given to illustrate the merits of the proposed approach. [ABSTRACT FROM AUTHOR]

We address the problem of classifying trajectories generated by dynamical systems. We consider the model-based approach, which is the classic approach in control theory, and (data-driven) support vector machines, a popular method in the area of machine learning. The analysis points out connections between the two approaches and their relative merits. Examples are given to substantiate the analysis. [ABSTRACT FROM AUTHOR]

We consider a decentralized networked control system (DNCS) consisting of a remote controller and a collection of linear plants, each associated with a local controller. Each local controller directly observes the state of its colocated plant and can inform the remote controller of the plant's state through an unreliable uplink channel. The downlink channels from the remote controller to local controllers were assumed to be perfect. The objective of the local controllers and the remote controller is to cooperatively minimize the infinite horizon time average of expected quadratic cost. The finite horizon version of this problem was solved in our prior work (“Optimal local and remote controllers with unreliable uplink channels,” IEEE, May 2019). The optimal strategies in the finite horizon case were shown to be characterized by coupled Riccati recursions. In this article, we show that if the link failure probabilities are below certain critical thresholds, then the coupled Riccati recursions of the finite horizon solution reach a steady state and the corresponding decentralized strategies are optimal. Above these thresholds, we show that no strategy can achieve finite cost. We exploit a connection between our DNCS Riccati recursions and the coupled Riccati recursions of an auxiliary Markov jump linear system to obtain our results. Our main result in Theorem explicitly identifies the critical thresholds for the link failure probabilities and the optimal decentralized control strategies when all link failure probabilities are below their thresholds. [ABSTRACT FROM AUTHOR]

In this article, we present two algorithms for identification of continuous-time linear time-invariant systems in frequency domain. These algorithms are constructed in terms of continuous rational orthogonal basis functions. First, a two-stage algorithm is developed through one-by-one selection of poles for the basis functions, and such consecutive selection is easy to realize. Next, a direct algorithm is proposed to select poles for the rational orthogonal basis functions. Different poles result in different bases and these selections guarantee that better approximations can be reached. For different systems, there are different sequences of poles selected for basis functions, which shows the adaptivity of the proposed algorithms. A numerical example is given to show that the proposed algorithms are useful. Also, in this example, comparison is made with the method that uses rational orthogonal basis functions in which all poles of the basis functions are true poles of the original system. [ABSTRACT FROM AUTHOR]

This article investigates global practical output tracking via adaptive output feedback for a class of uncertain nonlinear systems. Remarkably, the control problem under investigation is in the context of unknown control directions and output feedback, which severely restricts the system nonlinearities. Nevertheless, the growth on the unknown system nonlinearities in this article is extended from polynomial (of output) to arbitrary function, and meanwhile no further a priori information is required on the reference signal to be tracked. Specifically, sufficiently smooth pseudosign and pseudo-dead-zone functions are introduced acting as substitutions of sign and dead-zone functions in the literature, respectively. Typically, based on the pseudo-dead-zone function, a delicate estimate on the unknown system nonlinearities is established and a novel Lyapunov function is proposed. This, together with the elegant system performance analysis, is quite critical to remove the polynomial constraint and overcome the technical obstacle stemming from the essential extension. Additionally owing to the two refined functions, the use of smooth domination/treatment is moderately avoided in control design that enables the established control strategy to be tighter and less conservative. It turns out that under the proposed adaptive output-feedback controller, all the closed-loop system states are globally bounded, while the system tracking error enters a prescribed λ neighborhood of the origin in finite time and remains inside thereafter. A simulation example illustrates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The new concept of relative generic subsets is introduced. It is shown that the set of controllable linear finite-dimensional port-Hamiltonian systems is a relative generic subset of the set of all linear finite-dimensional port-Hamiltonian systems. This implies that a random, continuously distributed port-Hamiltonian system is almost surely controllable. [ABSTRACT FROM AUTHOR]

The Lyapunov–Krasovskii functional (LKF) method is an effective tool to obtain delay-dependent stability criteria of time-varying delay systems. However, in the method, the requirement that there must exist an appropriate LKF for a system with a delay varying in a delay interval is too strict and may lead to considerable conservativeness. In order to get less conservative stability criteria, a novel stability analysis method called a delay-mode-based LKF (DMBLKF) method is first presented for nonlinear delay systems. Compared with the LKF method, the main advantage of the DMBLKF method lies in relaxing the aforementioned requirement and leading to a less conservative criterion in stability analysis. Then, with the help of the novel method, new stability criteria of linear delay systems are derived. Finally, the effectiveness of the proposed method and the obtained criteria is illustrated through two numerical examples. [ABSTRACT FROM AUTHOR]

This article deals with computational complexity of various problems related to the zero controllability of a discrete-time linear time-invariant system, assuming that purely structural conditions at the level of the connections between the system states (i.e., state-connections) and the connections from the inputs to the states (i.e., input-connections) are known. Given a generically zero controllable system, we consider the following problems: i) find a minimal set of input-connections whose removal makes the resulting system not generic zero controllability; ii) identify a minimal cost set of input-connections that must be retained from the given set of input-connections while preserving generic zero controllability property; and iii) given a not generically zero controllable system, find a smallest set of state-connections whose removal makes the resulting system generically zero controllable. Problem i) is polynomially solvable. Problems ii) and iii) are NP-hard and approximation results are provided for them. The results of i) and iii) provide clues to analyze the fragility and hardness involved in modifying a system structure. Problem ii) is useful to ensure an accurate discrete-time linear approximation of a large-scale system by maintaining generic zero controllability of the linear system. [ABSTRACT FROM AUTHOR]