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This article considers linear discrete-time systems with additive disturbances and designs a model predictive control (MPC) law incorporating a dynamic feedback gain to minimize a quadratic cost function subject to a single chance constraint. The feedback gain is selected online, and we provide two selection methods based on minimizing upper bounds on predicted costs. The chance constraint is defined as a discounted sum of violation probabilities on an infinite horizon. By penalizing violation probabilities close to the initial time and assigning violation probabilities in the far future with vanishingly small weights, this form of constraints allows for an MPC law with guarantees of recursive feasibility without a boundedness assumption on the disturbance. A computationally convenient MPC optimization problem is formulated using Chebyshev’s inequality, and we introduce an online constraint-tightening technique to ensure recursive feasibility. The closed-loop system is guaranteed to satisfy the chance constraint and a quadratic stability condition. With dynamic feedback gain selection, the closed-loop cost is reduced and conservativeness of Chebyshev’s inequality is mitigated. Also, a larger feasible set of initial conditions can be obtained. Numerical simulations are given to show these results. [ABSTRACT FROM AUTHOR]

In this article, we aim at developing computationally tractable methods for nonlinear model/controller reduction. Recently, model reduction by generalized differential (GD) balancing has been proposed for nonlinear systems with constant input-vector fields and linear output functions. First, we study incremental properties in the GD balancing framework. Next, based on these analyses, we provide GD linear quadratic Gaussian (LQG) balancing and GD $H_\infty$ -balancing as controller reduction methods for nonlinear systems by focusing on linear feedback and observer gains. Especially for GD $H_\infty$ -balancing, we clarify when the closed-loop system consisting of the full-order system and a reduced-order controller is exponentially stable. All provided methods for controller reduction can be relaxed to linear matrix inequalities (LMIs). [ABSTRACT FROM AUTHOR]

This article investigates the problem of how to control nonlinear systems with delays in the state by memoryless linear feedback. The notions of semiglobal asymptotic stabilization and sublevel sets are introduced in the context of time-delay systems. With the aid of Razumikhin theorem, we develop a semiglobal design method for the construction of Lyapunov functions, associated sublevel sets, and delay-free linear state feedback laws, step-by-step, achieving semiglobal asymptotic stabilization for time-delay nonlinear systems in a lower triangular form. In contrast to the global stabilization of nonlinear systems with delays in the state, which is usually achieved by dynamic state feedback (Lin and Zhang, 2020), the significance of this work is to point out that a tradeoff of the control objectives, e.g., semiglobal versus global stabilization, makes it possible to control a class of time-delay nonlinear systems by static linear feedback. Extensions to nonlinear systems with globally asymptotically locally expoentially stable (GALES)-like inverse dynamics are also included in this article. [ABSTRACT FROM AUTHOR]

This article proposes a method for enlarging the region of attraction of linear model predictive controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the feasibility governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC-feedback law remains feasible. Offline polyhedral projection algorithms based on multiobjective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference. [ABSTRACT FROM AUTHOR]

The problem of global output tracking is addressed for stable minimum phase systems, with constant uncertain parameters and constant disturbances belonging to a known compact set, in the presence of input constraints such as amplitude saturation. The relative degree, the system order, and the sign of the high frequency gain are assumed to be known. A hybrid adaptive output feedback control is designed to achieve global asymptotic output tracking, provided that there exists an input within the input constraints capable of tracking exactly the output reference signal. By virtue of the hybrid control approach, the closed-loop system is linear within each time interval between parameter updating. Moreover, no information on input saturation is required by the controller. In addition to the standard assumptions in adaptive control design when inputs are unconstrained, further requirements on the reference signals, on system stability and on parameter bounds, are needed when inputs are constrained. [ABSTRACT FROM AUTHOR]

We investigate the implementation of a sparsitypromoting hands-off control scheme using the alternating direction method of multiplies (ADMM). In order to minimize the numerical control effort along with the actuation one, only a single ADMM iteration per time step is considered. We analyze the resulting closed-loop dynamics for linear systems with additive disturbances and show that the proposed scheme provides sparse controls as desired and, in addition, ensures input-to-state practical stability. We further point out a close relation between the proposed real-time scheme and (nonminimum time) dead-beat control. Finally, characteristics and effectiveness of the novel hands-off controller(s) are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

In robust control under state constraints, the set of admissible inputs is usually considered as given, under the assumption that the actuators have been already designed. However, if the input set is too small, any controller will fail in stabilizing the closed-loop system while satisfying all prescribed constraints for some initial states of interest, or vice versa the chosen actuators may be oversized. To handle this issue, in this article, we address the problem of computing the smallest input constraint set such that the closed-loop system is stabilizable from a prescribed set of initial states while respecting all constraints. We focus our attention on linear systems with additive disturbances, and develop the algorithm based on recursive feasibility of robust model predictive control. We demonstrate the results using numerical examples, in which we consider different metrics for the input constraint set selection. [ABSTRACT FROM AUTHOR]

This article investigates the event-triggered control problem for switched affine systems (SASs). The presence of affine terms brings many difficulties on the exclusion of triggering Zeno behavior when ensuring asymptotic stability. We propose an event-triggered control strategy dynamically updated with triggering to solve this problem, in which the triggering condition is associated with the affine terms and given with a time-varying term that is updated at triggering instants. Based on the triggering strategy, the controllers for subsystems and a switching rule are designed to achieve asymptotic stability of the resulting closed-loop system. Moreover, due to the special feature of event-triggered SASs, a new method for proving the exclusion of Zeno behavior is given. Finally, the developed results are illustrated by an electric circuit example. [ABSTRACT FROM AUTHOR]

This article deals with the input–output finite-time stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite-interval of time; therefore, the development and application of finite-time control methodologies is of particular relevance. The first contribution of this article is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of generalized difference Lyapunov equations; the latter allows one to establish the feasibility of an optimization problem by solving a set of difference linear matrix inequalities (DLMIs). The second contribution of this article is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

The Battistelli–Hespanha–Mosca–Tesi (BHMT) adaptive reset switching algorithm is enhanced to admit bumpless transfer and to control a nonlinear time-varying plant using the broad class of two-degree-of-freedom nonlinear time-varying controllers. Performance, including stability and exponential stability, is proved given only that the adaptive stabilization problem is $\lambda$ -feasible, which means at every time, there exists at least one exponentially stabilizing controller. We relax two restrictive BHMT assumptions: i) the plant is linear time-invariant (LTI) over most intervals and has finite order and ii) each controller is LTI. And, we expand the scope to include a broad class of bumpless switching algorithms. An example is provided to support the improved results. [ABSTRACT FROM AUTHOR]

This article presents a new optimization-based approach to determine the class of stabilizing control structures with the necessary set of feedback links for interconnected systems. The proposed approach relies on a graph-theoretic interpretation and its equivalence in terms of binary linear programs (BLPs). To carry out the primary goal, first, the stabilizability of a linear time-invariant (LTI) system under the decentralized control structure is presented in terms of a BLP. Next, two graph-based criteria are proposed to characterize stabilizing control structures with the required feedback links. Finally, all possible stabilizing control structures with the necessary feedback links are derived via solving a set of BLPs. In addition to the analysis of stabilizing control structures, the proposed graph-theoretic approach offers a versatile set of tools to find the simplest control structures capable of assigning the closed-loop spectrum in a totally arbitrary desired region. Simulation results illustrate the assessment of stabilizing control structures, the required additional feedback links, and the elegant generalization of the proposed approach to regional pole-placement. [ABSTRACT FROM AUTHOR]

This article proposes an event-triggered control design for cooperative control of heterogeneous multiagent systems. The design is serial in nature and consists of the design of a distributed event-triggered observer for each follower agent that estimates the desired information of the leader system in the presence of parametric uncertainty and, based on this observer, the design of a distributed event-triggered controller. A salient feature of our observer design is that it obeys the separation principle in the sense that the event-triggered control can be designed after the observer has been designed. As a result, the observer is applicable to different follower agent dynamics and the event-triggered time sequence for the controller is asynchronous of that of the observer. We implement this design scheme on linear heterogeneous multiagent systems and uncertain Euler–Lagrange multiagent systems, and achieve results that significantly extend the existing ones. [ABSTRACT FROM AUTHOR]

Given a centralized linear time-invariant (LTI) controller, this article investigates if and when the same can be implemented in a decentralized fashion using continuous-time, high-frequency, periodic controllers, recently reported in literature, without compromising input–output performance in averaged sense. In this regard, it is shown that for a strongly connected two-channel system having each subsystem of equal sizes, there exists a relation to compute the decentralized periodic controller gains in terms of the gains of a given centralized LTI controller if the latter is minimum-phase, stable, and satisfies some relative degree conditions. A method to satisfy this relative degree constraint while designing the centralized LTI controller is developed. A suitable example is considered to show that the proposed decentralized periodic controller can mimic a centralized LTI controller in averaged sense. At the end, it is found that the proposed decentralized periodic controller, however, does not have enough number of periodic gains to obtain the above relation to compute its parameters for systems with more than two channels. [ABSTRACT FROM AUTHOR]

Using the notion of exponential QSR-dissipativity (i.e., dissipativity with respect to a quadratic supply rate given in terms of real matrices Q, S,R), this article presents necessary and sufficient conditions for exponential stabilizability of nonlinear systems by linear static output feedback (SOF). It is shown that, under mild assumptions, the exponential stabilization of the closed-loop system around the origin is equivalent to the exponential QSR-dissipativity of the plant. Furthermore, whereas strict QSR-dissipativity is only sufficient for SOF asymptotic stabilization, it is proved to be necessary and sufficient for full state feedback control. New necessary and sufficient conditions for SOF stabilizability of linear systems are presented as well, along with a linear and noniterative semidefinite strategy for controller design. Necessary linear matrix inequality conditions for stabilization are also introduced. Some examples illustrate the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article considers the problem of output feedback stabilization for a class of nonlinear planar systems with unknown structures and measurements, which prevent the construction of conventional state observers. By taking advantage of the stability-increasing capability of a lead compensator, we propose a dynamic output feedback controller to globally stabilize the uncertain planar systems. For the special case of linear planar systems with unknown coefficients, a finite-time output feedback stabilizer based on a nonlinear compensator is constructed for a faster convergence rate. [ABSTRACT FROM AUTHOR]

We consider a version of the pole placement problem for one-sided linear discrete time-varying linear systems. Our purpose is to prove that uniform complete controllability is equivalent to possibility of arbitrary assignment of the dichotomy spectrum. [ABSTRACT FROM AUTHOR]

We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but noncausal, asymptotic regulation. A characterization of the problem solvability is deduced. We point out that the ideal problems cannot be solved in practice because they unrealistically require that the Brownian motion affecting the system is available for feedback. Drawing from the ideal solution, we formulate and solve approximate versions of the full-information and output-feedback problems, which do not yield perfect asymptotic tracking but can be solved in a realistic scenario. These solutions rely on two key ideas: First, we introduce a discrete-time a posteriori estimator of the variations of the Brownian motion obtained causally by sampling the system state or output; second, we introduce a hybrid state observer and a hybrid regulator scheme which employ the estimated Brownian variations. The approximate solution tends to the ideal as the sampling period tends to zero. The proposed theory is validated by the regulation of a circuit subject to electromagnetic noise. [ABSTRACT FROM AUTHOR]

This article studies the robust cooperative output regulation problem of heterogeneous uncertain linear multiagent systems under unbounded distributed transmission delays. A novel distributed observer is first proposed to estimate the state of an exosystem in the presence of unbounded distributed transmission delays. Then, two novel distributed controllers, one based on state feedback and the other based on output feedback, are further developed without any prior knowledge of the unbounded transmission delays. It is shown that the resulting closed-loop multiagent systems can achieve robust cooperative output regulation. It is also shown that the better transient performance is achieved with our proposed controllers in contrast to many existing low-gain controllers, which are proposed to deal with both bounded and unbounded transmission delays. Our results can be directly applied to solve cooperative output regulation problems of multiagent systems with bounded distributed or constant transmission delays. Furthermore, our results can also be directly applied to solve leader–following consensus problems of multiagent systems with unbounded distributed, bounded distributed, or constant transmission delays. Finally, a simulation example is provided to illustrate the effectiveness of the proposed controllers. [ABSTRACT FROM AUTHOR]

This article investigates the problem of designing $\mathcal {H}_{2}$ robust (or gain-scheduled) static output-feedback (or state-feedback) controllers for discrete-time positive linear systems affected by time-invariant (or time-varying) parameters belonging to a polytope. For this purpose, an iterative procedure based on robust (parameter-dependent) linear matrix inequalities (LMI) is proposed. Unlike most approaches, where the controller is obtained by means of a change of variables, the synthesis conditions deal with the control gain directly as an optimization variable, which is specially appealing to cope with closed-loop positivity or structural constraints. The existence of feasible initial conditions for the iterative procedure and some relaxation strategies adopted to reduce the conservativeness of the method are also discussed. Numerical examples borrowed from the literature and statistical comparisons show that the proposed technique is in general less conservative than other approaches, providing solutions and handling cases where traditional design techniques for positive systems cannot be applied. [ABSTRACT FROM AUTHOR]

The article presents distributed output feedback synthesis for both leaderless consensus and leader-follower consensus of linear multiagent systems subject to jointly connected switching networks. Luenberger type distributed observers are proposed based on the neighborhood output estimation error, and distributed output feedback controllers are developed according to the certainty equivalence principle. To show uniform global exponential stability of the switched closed-loop system, a separation principle for a class of switched linear systems with a cascaded structure is established employing weak Lyapunov function and checking weak zero-state detectability of its “diagonal” switched subsystems. It is shown that the weak zero-state detectability can be guaranteed by a generalized uniformly jointly connected condition of switching networks without any dwell-time constraints. [ABSTRACT FROM AUTHOR]

This article studies fixed-time stabilization (FxTS) of a general controllable linear system with an input delay $\tau$. It is shown that such a problem is not solvable if the prescribed convergence time $T_{\tau }$ is smaller than $2\tau$. For $T_{\tau }\geq 3\tau$ , a solution based on linear periodic delayed feedback (PDF) without any distributed delay is established. For $T_{\tau }>2\tau$ , a solution based on linear predictor-based PDF containing a distributed delay is proposed. For both cases, the gains of the PDF can be chosen as continuous, continuously differentiable, and even smooth, in the sense of infinitely many times differentiable. If only an output signal is available for feedback, two classes of linear observers with periodic coefficients are designed, so that their states converge to the current and future states of the system at a prescribed finite time, respectively. With the observed current and future states, FxTS can also be achieved by using, respectively, the PDF and observer-based PDF. A linear periodic feedback (without delay) is also established to solve the FxTS problem of linear systems with both instantaneous and delayed controls, which cannot be stabilized by any constant instantaneous feedback in certain cases. Two numerical examples verify the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article studies the problem of prescribed-time global stabilization of a class of nonlinear systems, where the nonlinear functions are unknown but satisfy a linear growth condition. By using solutions to a class of parametric Lyapunov equations containing a time-varying parameter that goes to infinity as the time approaches the prescribed settling time, linear time-varying feedback is designed explicitly to solve the considered problem, with the help of a Lyapunov-like function. It is shown moreover that the control signal is uniformly bounded by a constant depending on the initial condition. Both linear state feedback and linear observer-based output feedback are considered. The effectiveness of the proposed approach is illustrated by a numerical example borrowed from the literature. [ABSTRACT FROM AUTHOR]

This article presents an output feedback controller and observer design approach for linear time-invariant systems with unknown dynamics. The presented method uses an open-loop reference model to generate the desired trajectory and a closed-loop reference model as an observer. The controller only uses the observer states. Lyapunov-based stability proofs show that the error states converge asymptotically to zero and that all other signals are uniformly stable. Furthermore, bounds are proven on the transient behavior. [ABSTRACT FROM AUTHOR]

This article addresses the problem of controlling discrete-time linear time-invariant systems with parametric uncertainties in the presence of hard state and input constraints. A suitably designed gradient-descent-based indirect adaptive controller, used to handle parametric uncertainties, is combined with a model predictive control (MPC) algorithm, which guarantees constraint satisfaction. An estimated model of the actual uncertain plant is used for predictions of the future states. The parameters of the estimated model are updated using a gradient-descent-based adaptive update law. The errors arising due to the model mismatch between the estimated plant model and the actual uncertain plant are accounted for using a constraint tightening method in the MPC algorithm. The proposed adaptive MPC strategy is proved to be recursively feasible and the closed-loop system is proved to be bounded at all instants and asymptotically converging to the origin. [ABSTRACT FROM AUTHOR]

The stabilization problem for a class of nonlinear systems is solved via a novel method inspired by back-stepping. The method, that we call underactuated back-stepping, is introduced by solving the stabilization problem for an inertia wheel pendulum and it is then developed for a class of underactuated mechanical systems. The properties of the resulting closed-loop systems are studied in detail and case studies are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We consider the problem of designing a feedback controller for a multivariable linear time-invariant system, which regulates a system output to the solution of an equality-constrained convex optimization problem despite unknown constant exogenous disturbances; we term this the linear-convex optimal steady-state (OSS) control problem. We introduce the notion of an optimality model, and show that the existence of an optimality model is sufficient to reduce the OSS control problem to a stabilization problem. This yields a design framework for OSS control that unifies and extends existing design methods in the literature. We illustrate the approach via an application to optimal frequency control of power networks, where our methodology recovers centralized and distributed controllers reported in the recent literature. [ABSTRACT FROM AUTHOR]

In this article, we generalize previously reported results for linear, time-invariant, stabilizable multivariable systems described by a strictly proper transfer function matrix $P(s)$ with number of outputs greater than or equal to the number of inputs. By making use of a special kind of a left generalized inverse $P(s)_{\alpha }^{\oplus }$ of $P(s)$ , we define and examine the equivalent relation $\mathcal {R}$ relating $P(s)$ with the members of the equivalence class $[P(s)]_{R}$ of the closed loop-transfer function matrices $P_{C}(s)$ obtainable from $P(s)$ by the use of a proper compensator $C(s)$ in the feedback path. For $\mathcal {R}$ , we establish a set of complete invariants and a canonical form. These results give rise to a simple algorithmic procedure for the computation of proper internally stabilizing and denominator assigning compensators $C(s)$ for the class of plants with $p=m$ and having no zeros in the closed right half complex plane: $\mathbb {C}^{+}$ and in the case when $p>m$ plants characterized by right polynomial matrix fraction descriptions with a polynomial matrix numerator having at least one subset of $m$ rows that give rise to a nonsingular polynomial matrix with no zeros in $\mathbb {C}^{+}$. [ABSTRACT FROM AUTHOR]

We focus on the proportional-integral-derivative (PID) controller design for linear time-delay systems. All the controller gains ($k_P$ , $k_I$ , and $k_D$) and the delay ($\tau$) are treated as free parameters and no particular constraints are imposed on the controlled plants. Such a problem (involving totally four free parameters) is of theoretical as well as practical importance, but, to the best of the authors’ knowledge, it has not been fully explored. First, we will develop an algebraic algorithm to solve the complete stability problem w.r.t. $\tau$. Consequently, for any given PID controller vector $(k_P, k_I, k_D)$ , the distribution of ${NU}(\tau)$ (${NU}(\tau)$ denotes the number of characteristic roots in the right-half plane, as a function of $\tau$) can be accurately obtained and the exhaustive stability range of $\tau$ may be automatically calculated. Next, a global understanding of the distribution of ${NU}(\tau)$ over the whole $(k_P, k_I, k_D)$ -space may be achieved and all structural changes regarding the ${NU}(\tau)$ distribution can be analytically determined. To achieve such a goal, a complete positive real root classification (for some appropriate auxiliary characteristic equation) will be explicitly proposed. Finally, we will give a new methodology, a new parameter-space approach, for determining the stability set in the $(k_P, k_I, k_D, \tau)$ -space. [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]

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 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, 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 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]

We propose a constructive design method for linear systems with a nontrivial drift term, guaranteeing robust global asymptotic stability of the origin of the closed-loop system, as well as robust obstacle avoidance. To obtain discontinuous input actions, our controller is designed in the framework of hybrid systems. Using our proposed hybrid controller, we demonstrate that solutions do not enter a sphere, which we term an avoidance neighborhood, around specified isolated points. The constructive controller design methodology, as well as the closed-loop properties, is investigated via numerical examples. [ABSTRACT FROM AUTHOR]

This article deals with output feedback selection in linear time-invariant structured systems. We assume that the inputs and the outputs are dedicated, i.e., each input directly actuates a single state and each output directly senses a single state. Given a structured system with dedicated inputs and outputs and a cost matrix that denotes the cost of each feedback connection, our aim is to select a minimum cost set of feedback connections such that the closed-loop system satisfies arbitrary pole-placement. This problem is referred to as the optimal feedback selection problem for dedicated i/o. The optimal feedback selection problem for dedicated i/o is NP-hard and inapproximable to a constant factor of log n, where n denotes the system dimension. To this end, we propose an algorithm to find an approximate solution to the problem. The proposed algorithm consists of a potential function incorporated with a greedy scheme and attains a solution with a guaranteed approximation ratio. We consider two special network topologies of practical importance, referred to as back-edge feedback structure and hierarchical networks. For the first case, which is NP-hard and inapproximable to a multiplicative factor of log n, we provide a log n-approximate solution. For hierarchical networks, we give a dynamic programming based algorithm to obtain an optimal solution in polynomial time. [ABSTRACT FROM AUTHOR]

This article discusses the stability and stabilization problems for the discrete-time semi-Markov jump linear systems (S-MJLSs) with bounded sojourn times. By using the method of multiple-Lyapunov functions and the concept of discrete-time semi-Markov kernel, we provide the sufficient conditions for σ-error mean square stability of S-MJLSs. In such conditions, the transition probability matrix of embedded Markov chain is considered, which is more general than the scenarios in previous works that only consider the sojourn time of each subsystem mode. Based on such conditions, the stabilization controller design method is also proposed for the resulting closed-loop systems. Two examples are given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

A robust nonlinear control is designed for stabilizing linear multi-input–multi-output systems. The presented control law homogenizes a linear system (without its transformation to a canonical form) with a specified degree and stabilizes it in a finite time (or with a fixed-time attraction to any compact set containing the origin) if the degree of homogeneity is negative (positive). The tuning procedure is formalized in an linear matrix inequalities (LMI) form. Performance of the approach is illustrated by numerical and experimental examples. [ABSTRACT FROM AUTHOR]

Motivated by challenges in feedback control with event-triggered control input updates, this article studies an ellipsoidal set-valued feedback control problem for linear time-invariant (LTI) discrete-time (DT) systems, and its application to event-triggered control systems. First, a state feedback controller based on the set-valued information is designed for LTI DT systems with disturbances. Then, the stability of the closed-loop system is analyzed, and the state of the closed-loop system is shown to be uniformly ultimately bounded in an ellipsoidal set. Based on the proposed set-valued feedback controller, we consider the case when the event-triggering condition (ETC) is described by an ellipsoidal set for an event-triggered control system. To ensure the requirements on control performance and communication rates simultaneously, an optimal ETC design problem is formulated and its optimal solution is provided. Finally, simulation examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A systematic stabilization approach is provided for systems whose regulation error dynamics is subject to rational nonlinearities given prior knowledge of the system zero-error steady-state condition and a proper internal model. The error dynamics is cast in a differential-algebraic form so as to address the synthesis of controller parameters by a numerical optimization problem subject to bilinear matrix inequality constraints. A particular case is also explored where the resulting constraints are linear matrix inequalities. [ABSTRACT FROM AUTHOR]

A model matching and passivating control architecture for multi-input/multi-output linear systems, comprising dynamic feedback and feedforward, is proposed. The approach—essentially without any restriction on the relative degree and the zeros of the underlying system and by relying only on input/output measurements—provides a closed-loop system, the transfer matrix of which matches any desired matrix of rational functions. An alternative implementation of the above design allows to achieve an arbitrary approximation accuracy of a desired transfer matrix while also preserving structural properties—in particular observability—of the overall interconnected system. Such a construction can be then specialized to provide input/output decoupling or a system that is passive from a novel control input to a modified output. The result is achieved by arbitrarily assigning the relative degree and location of the poles and zeros on the complex plane of the interconnected system in a systematic way. It is also shown that similar ideas can be employed to enforce a desired, arbitrarily small, L2-gain from an unknown disturbance input to a modified output, while preserving the corresponding gain from the control input to the same output. The article is concluded with applications and further discussions on the results. [ABSTRACT FROM AUTHOR]

This article proposes a new high-frequency continuous-time two degrees of freedom (DOF) periodic control scheme to compensate linear time-invariant (LTI), square/nonsquare multivariable plants. The proposed scheme is more effective when the plant is nonminimum phase, or has more inputs than outputs. It is proved that, in averaged sense, the design of periodic controller can be recast as designing a 2-DOF LTI controller for an equivalent LTI plant. The conditions for which this equivalent plant becomes minimum phase are also obtained. When this plant is minimum phase and has no more inputs than outputs, the synthesis of the above-mentioned LTI controller is carried out using an linear matrix inequality-based $\mathcal {H}_{\infty }$ /loop transfer recovery (LTR) approach to achieve linear quadratic regulator (LQR) loop behavior asymptotically. The design method being based on LTR, the reference-input-to-output transfer function of the averaged compensated system becomes same as that using LQR. The periodic controller is shown to exhibit negligible ripples in the plant output, but $O(1)$ ripples in control input. Suitable examples are considered to show the superiority of the proposed control. [ABSTRACT FROM AUTHOR]

This paper addresses the event-triggered dynamic output feedback control for switched linear systems with frequent asynchronism. Different from existing work, which limits at most once switching during an interevent interval, we adopt the average dwell time approach without limiting the minimum dwell time of each subsystem, and thus frequent switching is allowed to happen in an interevent interval. Since the difficulty in acquiring the full information of system states, the dynamic output feedback controller is taken into account to stabilize the switched system. By employing a controller-mode-dependent Lyapunov functional, stability criterion is proposed for the resulting closed-loop system, based on which the dynamic output feedback controller together with the mode-dependent event-triggered mechanism is codesigned. Besides, the existence of the lower bound on interevent intervals is attentively discussed, which gets rid of the Zeno behavior. Finally, the effectiveness of the proposed method is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This note deals with the positivity-preserving consensus problem for undirected positive multiagent systems. The case that all agents have identical positive state-space models with multiple inputs is investigated. Using positive systems theory and analyzing the properties of the overall closed-loop system, positivity-preserving consensus conditions are derived. In order to preserve the positivity property of the agents, two conditions for positivity-preserving consensus are obtained. In contrast to some existing works that only give sufficient conditions for the solution, necessary and sufficient conditions are provided in this note. Then, the corresponding algorithm is developed for solution. Simulations are used to illustrate the effectiveness of the theoretical results and proposed algorithm. [ABSTRACT FROM AUTHOR]

A time delay present in the observation represents a mathematical challenge in an output feedback stabilization for linear infinite-dimensional systems. It is well known that for a linear hyperbolic system, a stabilizing output feedback control may become unstable when the observation has a time delay. For the fixed time delay in observation, the problem for one-dimensional partial differential equations (PDEs) has been solved by the observer-based feedback in the time interval where the observation is available and the predictor where the observation is not available. However, the generalization to multidimensional PDE systems has been a long-standing unsolved problem. In this paper, we investigate the problem from operator point of view for abstract first-order equation setting of infinite-dimensional systems. We formulate the problem in the framework of the well-posed and regular linear systems and solve it in the operator form. The result is then applied to the stabilization of a multidimensional Schrödinger equation. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing adaptive feedforward control (AFC) systems for uncertain single-input single-output linear systems perturbed by multisinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation is known for AFC to be applicable, which is referred to in this paper as a strictly positive real (SPR)-like condition. Notable features of the solution are that persistence of excitation is not required, and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented. [ABSTRACT FROM AUTHOR]

In this technical note, an adaptive model-predictive control (MPC) is proposed for a class of discrete-time linear systems with constant parametric uncertainties and control constraint. The proposed adaptive MPC originates from the principle of min–max optimization, which cannot be solved in a direct numerical way. An adaptive strategy is proposed to estimate the uncertain parameters, such that the estimated error converges, and the optimization in the MPC can be transferred into a solvable simple structure. Feasibility of the optimization and stability of the closed-loop system are proved theoretically, and a simulation example is presented to illustrate the theoretical result. [ABSTRACT FROM AUTHOR]

The overall dynamics of linear systems under pulsewidth modulated actuators is nonlinear, an inevitable fact that must be considered in designing feedback control for these systems. For small sampling periods, however, this nonlinearity is not severe, so that controller design can rely on the same techniques conventionally adopted for the linear systems. When a linear controller designed by these techniques is applied to the originally nonlinear system, it may not perform adequately at higher sampling periods. In particular, it may fail to stabilize the closed-loop system as predicted for a linear approximation of the original system. This paper introduces a class of nonlinear feedback laws outperforming their existing linear counterparts in terms of stability and transient response. The control laws in this class are nonlinearly modified forms of the linear quadratic (LQ) regulators and yield a closed-loop behavior similar to that of a linear system under a LQ regulator. As a result, the closed-loop dynamics is locally stable in essence, and will be globally stable under additional assumptions. As a case study, an inverted pendulum on a cart is stabilized using the proposed nonlinear control law. The superior performance of this control law over its linear counterparts is shown by numerical simulations. [ABSTRACT FROM AUTHOR]

We investigate integral input-to-state stability (iISS) of nonlinear networked control systems (NCSs). The controller is designed by emulation, i.e., it is constructed to ensure iISS for the closed-loop system in the absence of the network. Afterward, the latter is taken into account and explicit conditions are provided on the scheduling protocol and the maximum allowable transmission interval to preserve iISS for the NCS. The results are applied to two case studies: bilinear systems and neutrally stable linear systems under saturated feedback, where the conditions are formulated as linear matrix inequalities. The effectiveness of the results is further illustrated via a numerical example. [ABSTRACT FROM AUTHOR]

We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples. [ABSTRACT FROM AUTHOR]