By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Σ$ and a stochastic memoryless map $Ψ$. After that, we extend the result to the class of large scale systems in which: $Σ$ consists of many sub-systems; and $Ψ$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.
In this paper, the notion of robust strict QSR-dissipativity is applied to solve the static output feedback control problem for a class of continuous-time nonlinear rational systems subject to input saturation and bounded parametric uncertainties. A local dissipativity condition is combined with generalized sector conditions to formulate the synthesis of a stabilizing controller in terms of linear matrix inequalities. The strategy applies to general static output feedback design without any restrictions on the plant output equation. An iterative algorithm based on linear matrix inequalities is…
Economic Model Predictive Control (MPC) dissipativity theory is central to discussing the stability of policies resulting from minimizing economic stage costs. In its current form, the dissipativity theory for economic MPC applies to problems based on deterministic dynamics or to very specific classes of stochastic problems, and does not readily extend to generic Markov Decision Processes. In this paper, we clarify the core reason for this difficulty, and propose a generalization of the economic MPC dissipativity theory that circumvents it. This generalization focuses on undiscounted infinite-…
Non-overshooting stabilization is a form of safe control where the setpoint chosen by the user is at the boundary of the safe set. Exponential non-overshooting stabilization, including suitable extensions to systems with deterministic and stochastic disturbances, has been solved by the second author and his coauthors. In this paper we develop homogeneous feedback laws for fixed-time nonovershooting stabilization for nonlinear systems that are input-output linearizable with a full relative degree, i.e., for systems that are diffeomorphically equivalent to the chain of integrators. These homogen…
This paper is concerned with a compositional scheme for the construction of control barrier certificates for interconnected discrete-time stochastic systems. The main objective is to synthesize switching control policies against $ω$-regular properties that can be described by accepting languages of deterministic Streett automata (DSA) along with providing probabilistic guarantees for the satisfaction of such specifications. The proposed framework leverages the interconnection topology and a notion of so-called \emph{control sub-barrier certificates} of subsystems, which are used to composition…
This paper studies stochastic aperiodic stabilization of a networked control system (NCS) consisting of a continuous-time plant and a discrete-time controller. The plant and the controller are assumed to be connected by communication channels with i.i.d. time-varying delays. The delays are theoretically not required to be bounded even when the plant is unstable in the deterministic sense. In our NCS, the sampling interval is supposed to be determined directly by such communication delays. A necessary and sufficient inequality condition is presented for designing a state-feedback controller sta…
Control problems are always challenging since they arise from the real-world systems where stochasticity and randomness are of ubiquitous presence. This naturally and urgently calls for developing efficient neural control policies for stabilizing not only the deterministic equations but the stochastic systems as well. Here, in order to meet this paramount call, we propose two types of controllers, viz., the exponential stabilizer (ES) based on the stochastic Lyapunov theory and the asymptotic stabilizer (AS) based on the stochastic asymptotic stability theory. The ES can render the controlled …
