Search

When discrete-time Markov jump linear systems are prone to the damaging effects of polytopic uncertainties, it is necessary to address all the vertices of each Markov mode in order to properly design robust controllers. To this end, we propose a robust recursive linear–quadratic regulator for this class of systems. We define a quadratic min–max optimization problem by combining least-squares and penalty functions in a unified framework. We design a one-step cost function to encompass the entire set of vertices of each mode altogether, while maintaining its quadratic structure and the convexity of the problem. The solution is then obtained recursively and does not require numerical optimization packages. We establish conditions for convergence and stability by extending the matrix structure of the recursive solution. In addition, we provide numerical and real-world application examples to validate our method and to emphasize recursiveness and diminished computational effort. [ABSTRACT FROM AUTHOR]

Two stochastic model predictive control algorithms, which are referred to as distributionally robust model predictive control algorithms, are proposed in this article for a class of discrete linear systems with unbounded noise. Participially, chance constraints are imposed on both of the state and the control, which makes the problem more challenging. Inspired by the ideas from distributionally robust optimization (DRO), two deterministic convex reformulations are proposed for tackling the chance constraints. Rigorous computational complexity analysis is carried out to compare the two proposed algorithms with the existing methods. Recursive feasibility and convergence are proven. Simulation results are provided to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Linear complementarity system (LCS) consists of an ordinary differential equation (ODE) and a linear complementarity problem (LCP). In this article, we propose an exponential time-stepping method for solving LCS, which uses exponential integrator to discretize the ODE and solves the LCPs at the discrete time points. Numerical results are reported for illustrating its good performance. [ABSTRACT FROM AUTHOR]

The goal of this article is to investigate new and simple convergence analysis of dynamic programming for the linear–quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of both matrix inequalities and matrix norm. Under a mild assumption on the initial parameter, we prove that the $Q$ -value iteration exponentially converges to the optimal solution. Moreover, a global asymptotic convergence is also presented. These results are then extended to the policy iteration. We prove that in contrast to the $Q$ -value iteration, the policy iteration always converges exponentially fast. An example is given to illustrate the results. [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]

In this article, a noisy-output-based direct learning tracking control is proposed for stochastic linear systems with nonuniform trial lengths. The iteration-varying trial length is modeled using a Markov chain for demonstration of the iteration dependence. The effect of the noisy output is asymptotically eliminated using a prior given decreasing gain sequence in the learning algorithm. Two alternative adaptive gains are presented for improving the tracking performance and the convergence speed. Both the mean-square and almost-sure convergence are provided. Numerical simulations on a four-degree-of-freedom robot arm are presented to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This article presents a computational method to test the stabilizability of discrete-time switched linear systems. The existence of a conic cover of the space on whose elements a convex condition holds is proved to be necessary and sufficient for stabilizability. An algorithm for computing a conic partition that satisfies the new necessary and sufficient condition is given. The algorithm, which allows us to determine bounds on the exponential convergence rate, is proved to overcome the conservatism of conditions equivalent to periodic stabilizability and is applied to a 4-D system. [ABSTRACT FROM AUTHOR]

A finite-time observer for a class of linear time-varying systems with bounded unknown inputs is presented in this note. The design of the observer exploits structural properties of the system and, through a linear operator, allows applying the robust exact differentiator in a block form without requiring additional stabilizing terms. The proposed observer provides an exact estimate of the states after a finite transient time despite the possible instability of the system and the effects of bounded unknown inputs. [ABSTRACT FROM AUTHOR]

Recent studies have shown how regularization may play an important role in linear system identification. An effective approach consists of searching for the impulse response in a high-dimensional space, e.g., a reproducing kernel Hilbert space (RKHS). Complexity is then controlled using a regularizer, e.g., the RKHS norm, able to encode smoothness and stability information. Examples are RKHSs induced by the so-called stable spline or tuned-correlated kernels, which contain a parameter that regulates impulse response exponential decay. In this article, we derive nonasymptotic upper bounds on the $\ell _2$ error of these regularized schemes and study their optimality in order (in the minimax sense). Under white noise inputs and Gaussian measurement noises, we obtain conditions which ensure the optimal convergence rate for all the class of stable spline estimators and several generalizations. Theoretical findings are then illustrated via a numerical experiment. [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]

In this article, a robust nonlinear model reference adaptive control (MRAC) is proposed for disturbed linear systems, i.e., linear systems with parameter uncertainties, and external time-dependent perturbations or nonlinear unmodeled dynamics matched with the control input. The proposed nonlinear control law is composed of two nonlinear adaptive gains. Such adaptive gains allow the control to counteract the effects of some perturbations and nonlinear unmodeled dynamics ensuring asymptotic convergence of the tracking error to zero, and the boundedness of the adaptive gains. The nonlinear controller synthesis is given by a constructive method based on the solution of linear matrix inequalities. Besides, the simulation results show that, due to the nonlinearities, the rate of convergence of the proposed algorithm is faster than that provided by a classic MRAC. [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]

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increasingly relevant because they explicitly incorporate inherent uncertainty and variation in the system dynamics and thereby improve robustness properties of the controller. Robustness is a critical and poorly understood issue in reinforcement learning; existing methods which do not account for uncertainty can converge to fragile policies or fail to converge at all. Additionally, intentional injection of multiplicative noise into learning algorithms can enhance robustness of policies, as observed in ad hoc work on domain randomization. Although policy gradient algorithms require optimization of a nonconvex cost function, we show that the multiplicative noise LQR cost has a special property called gradient domination, which is exploited to prove global convergence of policy gradient algorithms to the globally optimum control policy with polynomial dependence on problem parameters. Results are provided both in the model-known and model-unknown settings where samples of system trajectories are used to estimate policy gradients [ABSTRACT FROM AUTHOR]

In this article, we deal with the consensus problem of multiple partial-state coupled linear systems, which are neutrally stable. These systems communicate over dynamic undirected networks, which change continuously and can be disconnected at any time. We develop an analysis framework from uniform complete observability theory to work out the necessary and sufficient conditions for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly if and only if a jointly $(\delta,T)$ -connected condition and an observability condition relying only on system and input matrices are satisfied. A lower bound of the convergence rate is also provided. We figure out the proof by applying matrix analysis and linear functional analysis. A simulation example is presented to illustrate our theoretical findings. [ABSTRACT FROM AUTHOR]

A novel approach to solve the problem of distributed state estimation of linear time-invariant systems is proposed in this article. It relies on the application of parameter-estimation-based observers, where the state observation task is reformulated as a parameter estimation problem. In contrast with existing results, our solution achieves convergence in finite time, without injection of high gain, and imposes very weak assumptions on the communication graph—namely, the existence of an open Hamiltonian walk. It is shown that this assumption is strictly weaker than the usual strong connectivity requirement. The scheme is shown to be robust vis-á-vis external disturbances and communication delays. [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 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]

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]

Due to their relevance in controller design, we consider the problem of determining the L2-gain, passivity properties, and conic relations of an input–output system. While, in practice, the input–output relation is often undisclosed, input–output data tuples can be sampled by performing (numerical) experiments. Hence, we present sampling strategies for discrete time and continuous time linear time-invariant systems to iteratively determine the L2-gain, the shortage of passivity and the cone with minimal radius that the input–output relation is confined to. These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input–output data samples. This leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time. [ABSTRACT FROM AUTHOR]

This article addresses the problem of robust observer design for nonlinear systems with transformed output. We first assume that there exists an observer design for a given nonlinear system. The structure of the system output is often crucial for estimating the system states. Therefore, we consider the problem that arises when the output is only available under a nonlinear transformation (affected by noise). This formulation is especially useful in engineering applications, where nonlinear sensors are frequent. We propose a new interconnected observer that estimates both the unavailable output and the system states, and we establish small-gain type conditions ensuring the asymptotic convergence of the overall error dynamics. To explicit our design parameters, we study the particular cases of state-affine systems up to output injection and systems with additive triangular nonlinearities. Finally, we provide corresponding numerical examples and comparisons with known observers. [ABSTRACT FROM AUTHOR]

This article is concerned with the moving horizon estimation (MHE) problem for networked linear systems (NLSs) with unknown inputs under dynamic quantization effects. For the NLSs with unknown input signals, the conventional MHE strategy is incapable of guaranteeing the satisfactory performance as the estimation error is dependent on the external disturbances. In this work, a novel MHE strategy is developed to cope with the underlying NLS with unknown inputs by dedicatedly introducing certain temporary estimates of unknown inputs, where the desired estimator parameters are designed to decouple the estimation error dynamics from the unknown inputs. A two-step design strategy (namely, decoupling step and convergence step) is proposed to obtain the estimator parameters. In the decoupling step, the decoupling parameter of the moving horizon estimator is designed based on certain assumptions on system parameters and quantization parameters. In the convergence step, by employing a special observability decomposition scheme, the convergence parameters of the moving horizon estimator are achieved such that the estimation error dynamics is ultimately bounded. Moreover, the developed MHE strategy is extended to the scenario with direct feedthrough of unknown inputs. Two simulation examples are given to demonstrate the correctness and effectiveness of the proposed MHE strategies. [ABSTRACT FROM AUTHOR]

This article is a comprehensive study of a long-observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use the Lambert W function to determine: 1) in what systems the delay can lead to increase in the rate of convergence; 2) the exact range of time delay, for which the rate of convergence is greater than that of the delay-free system; and 3) an estimate on the value of the delay that leads to the maximum rate of convergence. For the special case when the system matrix eigenvalues are all negative real numbers, we expand our results to show that the rate of convergence in the presence of delay depends only on the eigenvalues with minimum and maximum real parts. Moreover, we determine the exact value of the maximum rate of convergence and the corresponding maximizing time delay. We demonstrate our results through a numerical example on the practical application in accelerating an agreement algorithm for networked systems by using a delayed feedback. [ABSTRACT FROM AUTHOR]

To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this article, a theory of the approximate control of complex network systems is proposed and developed by the use of graphon theory and the theory of infinite dimensional systems. First, graphon dynamical system models are formulated in an appropriate infinite dimensional space in order to represent arbitrary-size networks of linear dynamical systems, and to define the convergence of sequences of network systems with limits in the space. Exact controllability and approximate controllability of graphon dynamical systems are then investigated. Second, the minimum energy state-to-state control problem and the linear quadratic regulator problem for systems on complex networks are considered. The control problem for graphon limit systems is solved in each case and approximations are defined which yield control laws for the original control problems. Furthermore, convergence properties of the approximation schemes are established. A systematic control design methodology is developed within this framework. Finally, numerical examples of networks with randomly sampled weightings are presented to illustrate the effectiveness of the graphon control methodology. [ABSTRACT FROM AUTHOR]

This article considers the problem of designing physical watermark signals in order to optimally detect possible replay attack in a linear time-invariant system, under the assumption that the system parameters are unknown and need to be identified online. We first provide a replay attack model, where an adversary replays the previous sensor data in order to fool the system. A physical watermarking scheme, which leverages a random input as a watermark to detect the replay attack, is then introduced. The optimal watermark signal design problem is cast as an optimization problem, which aims to achieve the optimal trade-off between control performance and intrusion detection. An online watermarking design and system identification algorithm is provided to deal with systems with unknown parameters. We prove that the proposed algorithm converges to the optimal one and characterize the almost sure convergence rate. An industrial process example is provided to illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

In this technical note, the tradeoff between the attack detectability and the performance degradation in stochastic cyber-physical systems is investigated. We consider a linear time-invariant system in which the attack detector performs a hypothesis test on the innovation of the Kalman filter to detect malicious tampering with the actuator signals. We adopt a notion of attack stealthiness to quantify the degree of stealth by limiting the maximum achievable exponents of both false alarm probability and detection probability below certain thresholds. And the conditions for any actuator attack to have a specific level of stealthiness are derived. Additionally, we characterize the upper bound of the performance degradation induced by attacks with a given extent of stealthiness that produces independent and identically distributed Gaussian innovations, and design the attack, which achieves the stated upper bound for right-invertible systems. Finally, our results are illustrated via numerical examples. [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 note considers the distributed optimal coordination (DOC) problem for heterogeneous linear multiagent systems. The local gradients are locally Lipschitz and the local convexity constants are unknown. A control law is proposed to drive the states of all agents to the optimal coordination that minimizes a global objective function. By exploring certain features of the invariant projection of the Laplacian matrix, the global asymptotic convergence is guaranteed utilizing only local interaction. The proposed control law is then extended with event-triggered communication schemes, which removes the requirement for continuous communications. Under the event-triggered control law, it is proved that no Zeno behavior is exhibited and the global asymptotic convergence is preserved. The proposed control laws are fully distributed, in the sense that the control design only uses the information in the connected neighborhood. Furthermore, to achieve the DOC for linear multiagent systems with unmeasurable states, an observer-based event-triggered control law is proposed. A simulation example is given to validate the proposed control laws. [ABSTRACT FROM AUTHOR]

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

To solve a time-varying overdetermined problem, a novel varying-parameter convergent-differential neural network (VP-CDNN) is proposed, designed, and discussed. Specifically, a vector-error function is first defined. Second, according to neural dynamic design method, an implicit-dynamic equation with a time-varying parameter is derived. Mathematics analysis and theoretical proof verify that the VP-CDNN can obtain the least-squares solution with a super exponential convergence rate. In addition, it is also proved that VP-CDNN can restrain the noise efficiently. Simulations among the VP-CDNN, gradient-based recurrent neural network and zeroing neural network verify that the VP-CDNN has faster speed, higher accuracy, and stronger robustness. At last, applications to data fitting and system identification further verify the high effectiveness and efficiency of the VP-CDNN. [ABSTRACT FROM AUTHOR]

Periodic orbits often describe desired state trajectories of dynamical systems in various engineering applications. Stability analysis of periodic solutions lays a foundation for control design to achieve convergence to a prescribed orbit. Here we consider a class of perturbed nonlinear systems with fast and slow dynamics and develop a novel averaging method for analyzing the local exponential orbital stability of a periodic solution. A framework is then proposed for feedback control design to stabilize a natural oscillation of an uncertain nonlinear system using a synchronous adaptive oscillator. The idea is applied to linear mechanical systems and a design theory is established. In particular, we propose a controller based on the Andronov–Hopf oscillator with additional adaptation mechanisms for estimating the unknown natural frequency and damping parameters. We prove that, with sufficiently slow adaptation, the estimated parameters locally converge to their true values and entrainment to the natural oscillation is achieved as part of an orbitally stable limit cycle. Numerical examples demonstrate that adaptation and convergence can in fact be fast. [ABSTRACT FROM AUTHOR]

This paper proposes an approximate/adaptive optimal control (AOC) design for completely unknown continuous-time linear time invariant systems, without requiring the restrictive persistence of excitation (PE) condition for parameter convergence. The proposed AOC algorithm utilizes two layers of filtering—the first layer filters strategically eliminate the need for state derivative information, while the second layer filters provide suitable algebraic relations for iteratively obtaining the optimal policy under a milder online-verifiable initial excitation assumption. Unlike previous AOC algorithms, the proposed method does not require finite window integrals, intelligent data-storage, and the restrictive PE assumption. Further, the proposed method relaxes the sufficient condition required for obtaining successive stabilizing control policies. The intermediate policies are proved to be stabilizing and converging to the optimal policy. Simulation results validate the efficacy of the proposed adaptive/approximate linear quadratic regulator algorithm. [ABSTRACT FROM AUTHOR]

In this technical note, a distributed algorithm is proposed for multiagent networks to achieve a least squares solution of a system of linear equations, in which each agent only knows part of the overall equations and communicates only with its nearby neighbors. The proposed algorithm is discrete time but does not involve small or time-varying step sizes. Given that the network is fixed, connected, and undirected, the proposed algorithm enables all agents in the network to achieve exponentially fast the same least squares solution; this is validated by simulations. [ABSTRACT FROM AUTHOR]

An adaptive algorithm solving the on-line parameter estimation problem for a broad class of linear systems is proposed. The approach can be applied to systems with delay, distributed-parameter systems, fractional-order systems, and others that are stable or stabilized by linear feedback. The proposed scheme can be applied to simultaneously track sufficiently slow changes in process gains, delays, time constants, diffusivity, and other parameters. The proposed method is gradient-based, and it yields a relatively efficient numerical implementation. Convergence and robustness of the algorithm are investigated through Lyapunov analysis, yielding explicit convergence conditions that generalize the well-known “persistence of excitation” and identifiability requirements arising in conventional adaptive estimation. The method is illustrated by several examples. [ABSTRACT FROM AUTHOR]

For linear systems in the observer canonical form, we introduce a state observer with time-varying gains that tend to infinity as time approaches a prescribed convergence time. The observer is shown to exhibit fixed-time stability with an arbitrary convergence time, which is prescribed by the user irrespective of initial conditions. The output estimation error injection terms are also shown to remain uniformly bounded and converge to zero at the prescribed time. [ABSTRACT FROM AUTHOR]

Model reference adaptive control is a well-understood and popular method used in the case when the plant's constant parameters are unknown and must be identified. The related literature is very rich and there exist many proofs of stability and convergence. Lyapunov functions for such systems, having the property that the total derivative is negative definite, are, however, very scarce. In this note, we use the Mazenc construction to design a simple strict Lyapunov function in a rather intuitive manner, based on a first-choice function whose derivative is negative semidefinite. Furthermore, we provide, for the first time in the literature, a Lyapunov function for a popular passivity-based adaptive controller for Lagrangian systems. [ABSTRACT FROM AUTHOR]

This paper studies linear stochastic approximation (SA) algorithms and their application to multiagent systems in engineering and sociology. As main contribution, we provide necessary and sufficient conditions for convergence of linear SA algorithms to a deterministic or random final vector. We also characterize the system convergence rate, when the system is convergent. Moreover, differing from non-negative gain functions in traditional SA algorithms, this paper considers also the case when the gain functions are allowed to take arbitrary real numbers. Using our general treatment, we provide necessary and sufficient conditions to reach consensus and group consensus for first-order discrete-time multiagent system over random signed networks and with state-dependent noise. Finally, we extend our results to the setting of multidimensional linear SA algorithms and characterize the behavior of the multidimensional Friedkin–Johnsen model over random interaction networks. [ABSTRACT FROM AUTHOR]

In this paper, the problem of convergence for the optimal linear estimator of discrete-time linear systems with multiplicative and time-correlated additive measurement noises is studied. By defining a new random vector that consists of the innovation, error, and part of the noise in the new measurement obtained from the measurement differencing method, we obtain convergence conditions of the optimal linear estimator by equivalently studying the convergence of the expectation of a random matrix where the random matrix is the product of the new vector and its transpose. It is also shown that the state error covariance matrix of the optimal linear estimator converges to a unique fixed point under appropriate conditions and, moreover, this fixed point can be obtained by solving a set of matrix equations. [ABSTRACT FROM AUTHOR]

This technical note considers a consensus problem of high-order multiagent systems with antagonistic interactions and communication noises. The interaction network associated with the multiagent system is modeled by a signed graph (called coopetition network) and the agent dynamics is described by a general linear system. A novel stochastic-approximation based control strategy is designed for each agent by using the relative state information from its neighbors. Additionally, convergence of a consensus error system is analyzed by the stochastic stability theory. Finally, the effectiveness of our results is demonstrated by simulation. [ABSTRACT FROM AUTHOR]

This paper focuses on the design of an asynchronous dual solver suitable for model predictive control (MPC) applications. The proposed solver relies on a state-of-the-art variance reduction (VR) scheme, previously used in the context of proximal stochastic gradient methods (Prox-SVRG) and on the alternating minimization algorithm (AMA). The resultant algorithm, a stochastic AMA with VR (SVR-AMA), shows geometric convergence (in the expectation) to a suboptimal solution of the MPC problem and, compared to other state-of-the-art dual asynchronous algorithms, allows one to tune the probability of the asynchronous updates to improve the quality of the estimates. Two novel accelerated versions of the Prox-SVRG (and, by duality, of SVR-AMA) are also provided. We apply the proposed algorithm to a specific class of splitting methods, that is, the decomposition along the length of the prediction horizon. Numerical results on the longitudinal control problem of an Airbus passenger aircraft show the benefits that we can gain in terms of computation time when using our proposed solver with an adaptive probability distribution. [ABSTRACT FROM AUTHOR]

This paper provides an extension of the observability rank condition to nonlinear systems driven by both known and unknown inputs. In particular, the systems here considered are characterized by dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input (or disturbance) and multiple known inputs. Additionally, it is assumed that the unknown input is a differentiable function of time (up to a given order). The goal of the paper is not to design new observers for these systems but to provide the analytic condition in order to check the weak local observability of the state. This condition is simple and can be easily and automatically applied to the nonlinear systems mentioned above, independently of their complexity and type of nonlinearity. In particular, the complexity of the analytic condition is comparable to the complexity of the standard method to check the state observability in the case without unknown inputs (i.e., the observability rank condition). This is a fundamental practical (and unexpected) advantage. As for the observability rank condition, the proposed analytic condition is based on the computation of the observable codistribution. Similarly to the case of only known inputs, the observable codistribution is obtained by recursively computing the Lie derivatives of the outputs along the vector fields that characterize the dynamics. However, in correspondence of the unknown input, the corresponding vector field must be suitably rescaled. Additionally, the Lie derivatives of the outputs must also be computed along a new set of vector fields that are obtained by recursively performing suitable Lie bracketing of the vector fields that define the dynamics. In practice, the entire observable codistribution is obtained by a very simple recursive algorithm. Finally, it is shown that the recursive algorithm converges in a finite number of steps, and the criterion to establish that the convergence has been reached is provided. The proposed analytic extension of the observability rank condition is illustrated by checking the weak local observability of several nonlinear systems driven by known inputs and a single disturbance. [ABSTRACT FROM AUTHOR]

We consider a version of the pole assignment problem for linear discrete time-varying systems with linear state feedback. Our aim is to prove that all the systems from the closure (in the topology of pointwise convergence) of all shifts of the original system have an assignable Lyapunov spectrum if and only if the original system is uniformly completely controllable. We also provide an example to show that uniform complete controllability is not a necessary condition for assignability of the Lyapunov spectrum of the original system. [ABSTRACT FROM AUTHOR]

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

This paper deals with the stabilization of linear systems with process noise under packet drops between the sensor and the controller. Our aim is to ensure exponential convergence of the second moment of the plant state to a given bound in finite time. Motivated by considerations about the efficient use of the available resources, we adopt an event-triggering approach to design the transmission policy. In our design, the sensor's decision to transmit or not is based on an online evaluation of whether the control objective may be violated in the future. The resulting event-triggering policy is hence specifically tailored to the control objective. We formally establish that the proposed event-triggering policy meets the desired objective and quantify its efficiency by providing an upper bound on the fraction of expected number of transmissions in an infinite time interval. Simulations for scalar and vector systems illustrate the results. [ABSTRACT FROM AUTHOR]

We solve the problem of stabilizing a general class of linear first-order hyperbolic systems using actuation at both boundaries of the spatial domain. We design a novel Fredholm transformation similarly to backstepping approaches to derive a boundary controller and a boundary observer enabling stabilization by output feedback. This yields an explicit full-state feedback law that achieves the theoretical lower bound for convergence to zero. [ABSTRACT FROM AUTHOR]

The problem of convergent fault estimation for a class of linear systems with faults and disturbances is addressed for the first time in this technical note. A differential-equation-based convergence theorem of mean sequence of estimates is proposed, which provides an iterative mean estimation technique that has not been fully reported yet in the literature. Based on the technique, a convergent fault estimation strategy for the linear system in consideration is designed, and the convergence of mean sequence of fault estimates is proved theoretically. An iterative algorithm is given subsequently to compute the fault estimates. Numerical simulation results demonstrate the effectiveness and merits of the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the performance analysis and synthesis of distributed system throttlers (DST). A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. This can be used to protect a service's backend/clients from getting overloaded, or to reduce the effects of uncertainties in demand for shared services. We study performance deterioration of DSTs subject to demand uncertainty. We then consider network synthesis problems that aim to improve the performance of noisy DSTs via communication link modifications as well as server update cycle modifications. [ABSTRACT FROM PUBLISHER]

Sufficient conditions for the existence and convergence to zero of numeric approximations to solutions of asymptotically stable homogeneous systems are obtained for the explicit and implicit Euler integration schemes. It is shown that the explicit Euler method has certain drawbacks for the global approximation of homogeneous systems with nonzero degrees, whereas the implicit Euler scheme ensures convergence of the approximating solutions to zero. Properties of absolute and relative errors of the respective discretizations are investigated. [ABSTRACT FROM AUTHOR]

In the paper “ISS with respect to boundary disturbances for 1-D parabolic PDEs” (IEEE Transactions on Automatic Control, vol. 61, pp. 3712–3724, 2016), input-to-state stability properties are established for 1-D spatially varying parabolic partial differential equations (PDEs) under certain assumptions, imposed on eigenvalues and eigenfunctions of an associated Sturm–Liouville operator. A key assumption on the absolute convergence of an associated Fourier series, composed of the normalized eigenfunctions and inverse eigenvalues of the Sturm–Liouville operator, is analyzed in the present note. General properties of the Sturm–Liouville operator are carried out to demonstrate that such a key assumption becomes redundant for the underlying PDEs with sign-definite sufficiently smooth coefficients. [ABSTRACT FROM PUBLISHER]

We employ our recent discrete-time stochastic averaging theorems and stochastic extremum seeking to iteratively (batch-to-batch) optimize open-loop control sequences for unknown but reachable discrete-time linear systems with a scalar input and without known system dimension, for a cost that is quadratic in the measurable output and the input. First, for a multivariable gradient-based stochastic extremum seeking algorithm we prove local exponential convergence to the optimal open-loop control sequence. Second, to remove the convergence rate's dependence on the Hessian matrix of the cost function, which is unknown since the system's model (the system matrices $(A,B,C)$) is unknown, we develop a multivariable discrete-time Newton-based stochastic extremum seeking method, design the Newton-based algorithm for the iteration of the input sequence, and prove local exponential convergence to the optimal input sequence. Finally, two simulation examples are given to illustrate the effectiveness of the two methods. [ABSTRACT FROM AUTHOR]

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set, while the second method provides an inner approximation. The outer approximation scheme is $\delta$ -complete, given that the constraint sets are formulated as finite unions of polytopes. [ABSTRACT FROM AUTHOR]