Systems & Control Letters最新文献

Decentralized stochastic control problems with local information involve problems where multiple agents and subsystems which are coupled via dynamics and/or cost are present. Typically, however, the dynamics of such couplings is complex and difficult to precisely model, leading to questions on robustness in control design. Additionally, when such a coupling can be modeled, the problem arrived at is typically challenging and non-convex, due to decentralization of information. In this paper, we develop a robustness framework for optimal decentralized control of interacting agents, where we show that a decentralized control problem with interacting agents can be robustly designed by considering a risk-sensitive version of non-interacting agents/particles. This leads to a tractable robust formulation where we give a bound on the value of the cost function in terms of the risk-sensitive cost function for the non-interacting case plus a term involving the “strength” of the interaction as measured by relative entropy. We will build on Gaussian measure theory and an associated variational equality. A particular application includes mean-field models consisting of (a generally large number of) interacting agents which are often hard to solve for the case with small or moderate numbers of agents, leading to an interest in effective approximations and robustness. By adapting a risk-sensitivity parameter, we also robustly control a non-symmetrically interacting problem with mean-field cost by one which is symmetric with a risk-sensitive criterion, and in the limit of small interactions, show the stability of optimal solutions to perturbations.

This paper introduces novel methods for analyzing the stability of impulsive switched systems with bounded sojourn time intervals. We contend that existing stability results may be overly conservative when sojourn times are treated as stochastic rather than arbitrary over intervals. This motivates our investigation into stochastic stability criteria for impulsive switched systems, where the sojourn times of impulsive switching signals obey uniform distributions over intervals. Our first theoretical contribution offers an exact formula for the component-wise first moment of the state for linear impulsive switched systems, expressed in terms of a solution to an auxiliary linear time-delay system. We extend this approach to nonlinear systems by leveraging a multiple Lyapunov function assumption. Consequently, the exponential mean stability of such impulsive switched systems can be determined by assessing the stability of the auxiliary systems. Nevertheless, this method fails to establish exponential mean stability when the impulsive switched system has unstable subsystems. To address this limitation, we conduct an in-depth frequency domain analysis, revealing a common occurrence of pole-zero cancellation. Leveraging these insights, we propose a non-conservative approach for stability analysis. Simulations demonstrate that our proposed stability criteria effectively determine stability in scenarios where all subsystems are unstable, or instability when all subsystems are stable.

We consider the problem of achieving prescribed-time stability (PT-S) in a class of hybrid dynamical systems that incorporate switching nonlinear dynamics, exogenous inputs, and resets. By “prescribed-time stability”, we refer to the property of having the main state of the system converge to a particular compact set of interest before a given time defined a priori by the user. We focus on hybrid systems that achieve this property via time-varying gains. For continuous-time systems, this approach has received significant attention in recent years, with various applications in control, optimization, and estimation problems. However, its extensions beyond continuous-time systems have been limited. This gap motivates this paper, which introduces a novel class of switching conditions for switching systems with resets that incorporate time-varying gains, ensuring the PT-S property even in the presence of unstable modes. The analysis leverages tools from hybrid dynamical system’s theory, and a contraction–dilation property that is established for the hybrid time domains of the solutions of the system. We present the model and main results in a general framework, and subsequently apply them to two different problems: (a) PT control of dynamic plants with uncertainty and intermittent feedback; and (b) PT decision-making in non-cooperative switching games using algorithms that incorporate momentum, resets, and dynamic gains. Numerical results are presented to illustrate all our results.

Classically rigid-motion kinematics are formulated on the Special Euclidean Group or parameterizations of that group. However, this is an approximation of the true configuration space evolving in space–time. Moreover, the Special Euclidean Group provides a sufficiently accurate approximation to a rigid-motion when moving at non-relativistic speeds. Here we present a setting which generalizes a rigid-motion in Euclidean space to rigid-motion in space–time. A kinematic feedback law is presented and proved to almost globally stabilize a rigid-motion in space–time. This setting defines the kinematics on a class of Lie group whose inverse is a function of its transpose and associated metric tensor. It is shown that the Special Euclidean Group is a limiting case of this class of Lie group and this alternative viewpoint can be utilized in stability proofs for rigid-motion kinematic control. An example control design and stability proof on this general class of Lie group is demonstrated.

We present a method for estimating the domain of attraction of a discrete-time system with uncertainty. Difference inclusions are used to model the system’s dynamics. Two conditions (invariance and negative definiteness) are derived in terms of the Lyapunov stability of the systems. We propose an interval version of the Lyapunov equation, which ensures the negative definiteness for a given Lyapunov function. Then, we introduce some sufficient conditions for invariance. Finally, the estimation of the domain of attraction is extended by solving an optimization problem. These results do not assume that the Lyapunov function is quadratic and can be fully applied even in the presence of control input saturation and uncertainty, such as aperiodic sampled-data. Some numerical examples validate the method and compare it with other approaches presented in this work.

This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input–state–output or input–output data based on whether the state is measurable. To remove the need for the persistently exciting (PE) condition of a sufficiently high order on pre-collected data, a set containing all systems capable of generating such data is constructed. Then, at each time step, an upper bound on a given objective function is derived for all systems in the set, and a feedback controller is designed to minimize this bound. The optimal control gain at each time step is determined by solving a set of linear matrix inequalities. We prove that if the synthesis problem is feasible at the initial time step, it remains feasible for all future time steps. Unlike current data-driven predictive control schemes based on behavioral system theory, our approach requires less stringent conditions for the pre-collected data, facilitating easier implementation. The effectiveness of our proposed methods is demonstrated through application to an unknown and unstable batch reactor.

In this paper, we consider the non-collocated stabilization of three coupled wave equations with different speeds and joint anti-dampings. These anti-dampings put all eigenvalues of the system in the right complex plane. By designing two invertible transformations, the wave system is converted into an equivalent system with damping terms at the joint points. The feedback controllers with displacements/velocities are designed to obtain the target system. The well-posedness and exponential stability of the closed-loop system are established using the PDE approach, based on the exponential stability of the target system. Simulation results are presented to verify the effectiveness of the feedback control law.

We use a deterministic model to study two competing viruses spreading over a two-layer network in the Susceptible–Infected–Susceptible (SIS) framework, and address a central problem of identifying the winning virus in a “survival-of-the-fittest” battle. Almost all existing conditions ensure that the same virus wins regardless of initial states. In the present paper, we ask the following question: can we systematically construct SIS bivirus networks with an arbitrary but finite number of nodes such that either of the viruses can win the survival-of-the-fittest battle, depending on the initial states? We answer this question in the affirmative. More specifically, we show that given almost any network layer of one virus, we can (using our proposed systematic four-step procedure) construct the network layer for the other virus such that in the resulting bivirus network, either of the two viruses can win the survival-of-the-fittest battle. Conclusions from numerical case studies, including a real-world mobility network that captures the commuting patterns for people between 107 provinces in Italy, illustrate and extend the theoretical result and its consequences.

In this paper, we study the $\sigma$-error moment stability and stabilization for a class of discrete-time semi-Markov jump linear systems (S-MJLS). It is shown that the existing results on $\sigma$-error moment stability for discrete-time S-MJLS can be obtained under weaker conditions, and based on the established stability results, the high-order moment stabilization problem is investigated for the first time.

We develop a switched predictor-feedback law, which achieves global asymptotic stabilization of linear systems with input delay and with the plant and actuator states available only in (almost) quantized form. The control design relies on a quantized version of the nominal predictor-feedback law for linear systems, in which quantized measurements of the plant and actuator states enter the predictor state formula. A switching strategy is constructed to dynamically adjust the tunable parameter of the quantizer (in a piecewise constant manner), in order to initially increase the range and subsequently decrease the error of the quantizers. The key element in the proof of global asymptotic stability in the supremum norm of the actuator state is derivation of solutions’ estimates combining a backstepping transformation with small-gain and input-to-state stability arguments, for addressing the error due to quantization. We extend this result to the input quantization case and illustrate our theory with a numerical example.