Yulong Gao

Cooperative distributed stochastic MPC for systems with state estimation and coupled probabilistic constraints

A cooperative distributed stochastic model predictive control (CDSMPC) algorithm is given for multiple dynamically decoupled subsystems with additive stochastic disturbances and coupled probabilistic constraints, for which states are not measurable. Cooperation between subsystems is promoted by a scheme in which a local subsystem designs hypothetical plans for others in some cooperating set, and considers the weighted costs of these subsystems in its objective. To achieve satisfaction of coupled probabilistic constraints in a distributed way, only one subsystem is permitted to optimize at each time step. In addition, by using a lifting technique and the probabilistic information on additive disturbances, measurement noise and the state estimation error, a set of deterministic constraints is constructed for the predictions of nominal models. Recursive feasibility with respect to both local and coupled probabilistic constraints is guaranteed and stability for any choice of update sequence and any structure of cooperation is ensured. Numerical examples illustrate the efficacy of the proposed algorithm.

Distributed Stochastic MPC of Linear Systems With Additive Uncertainty and Coupled Probabilistic Constraints

This technical note develops a new form of distributed stochastic model predictive control (DSMPC) algorithm for a group of linear stochastic subsystems subject to additive uncertainty and coupled probabilistic constraints. We provide an appropriate way to design the DSMPC algorithm by extending a centralized SMPC (CSMPC) scheme. To achieve the satisfaction of coupled probabilistic constraints in a distributed manner, only one subsystem is permitted to optimize at each time step. In addition, by making explicit use of the probabilistic distribution of the uncertainties, probabilistic constraints are converted into a set of deterministic constraints for the predictions of nominal models. The distributed controller can achieve recursive feasibility and ensure closed-loop stability for any choice of update sequence. Numerical examples illustrate the efficacy of the algorithm.

Distributed MPC for formation of multi-agent systems with collision avoidance and obstacle avoidance

Abstract The paper is concerned with the problem of distributed model predictive control (DMPC) for formation of multiple linear second-order agents with collision avoidance and obstacle avoidance. All the agents are permitted to implement optimization simultaneously at each time step. The assumed input trajectory and state trajectory are introduced to obtain a computationally tractable optimization problem in a distributed manner. As a result, a compatibility constraint is required to ensure the consistency between each agent׳s real operation and its plan and to establish the agreement among agents. The terminal ingredients are tailored by making use of the specific form of the system model and the control objective. The terminal set is ensured to be positively invariant with the designed terminal controller. The collision avoidance constraint and the obstacle avoidance constraint are satisfied for any state in the terminal set. The weighted matrix of the terminal cost is determined by solving a Lyapunov equation. Moreover, recursive feasibility of the resulting optimization problem is guaranteed and closed-loop stability of the whole system is ensured. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

Stochastic self-triggered model predictive control for linear systems with probabilistic constraints

A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.

Data-Driven Filter Design for Linear Networked Systems with Bounded Noise

Considering the case that the mathematical model of control plant is unavailable, this paper is concerned with the problem of data-driven filtering for linear networked systems with bounded noise and transmission data dropouts. One merit of the design is that the filter can be directly employed without identifying the model. To overcome the effect of data dropouts during the transmission, an output predictor is designed based only on the received output and input of the system. By utilizing the predicted output, a direct worst-case almost-optimal filter within the set membership framework is presented.

Network-Based Data-Driven Filtering With Bounded Noises and Packet Dropouts

This paper is concerned with the problem of a network-based data-driven filter design for discrete-time linear systems with bounded noises and packet dropouts. One favorable feature is that the designed filter can be directly employed without identifying the unknown system model. To compensate the negative effects of packet dropouts, an output predictor is first designed to reconstruct the missing data based on the received outputs and the inputs of the system. The asymptotic convergence of the output prediction error is established, of which the rate can be adjusted by the parameter. Then utilizing the predicted outputs and the received measurements, an almost-optimal data-driven filter with tractability is proposed within the set membership (SM) framework and the bound on the worst case estimation error is derived. Finally, two illustrative examples, including a comparison example and an application example, are presented to show the advantages of the proposed design and the effectiveness of the theoretical results.