Distributed Model Predictive Control and Optimization for Linear Systems With Global Constraints and Time-Varying Communication

Abstract

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.Index Terms-Distributed model predictive control (DMPC), global constraints, gossip-based push-sum algorithm, push-sum dual gradient (PSDG) algorithm, time-varying directed graphs.

Mini-batch stochastic three-operator splitting for distributed optimization

“…where f : R n → R is a convex and continuously differentiable function, g : R n → (−∞, ∞] and h : R m → (−∞, ∞] are closed convex and lower semi-continuous functions, and L : R n → R m is a given linear map. Such a structure is very general, and and describes many applications that range from signal processing to machine learning to control [1], [2], [3]. In many instances of problem (1), the cost functions are contaminated by stochastic noise.…”

“…Such a structure is very general, and and describes many applications that range from signal processing to machine learning to control [1], [2], [3]. In many instances of problem (1), the cost functions are contaminated by stochastic noise. In such settings, we are given a probability space (Ω, A, P) carrying a random variable ξ : Ω → Ξ ⊂ R d , and a measurable function F : R n × Ξ → R so that…”

“…The presence of stochastic uncertainty challenges any direct solution method for problem (1), since the smooth function f is not directly accessible in practice, unless the distribution of the random variable is known. Indeed, the expectation (2) cannot be computed exactly, and instead we need to restore to simulation-based techniques.…”

Two-layer nonlinear control of DC-DC buck converters with meshed network topology

“…A common feature of both approaches is that they both require some degree of cooperation between the elements of the network. This is particularly useful when global constraints exists as shown by Jin et al (2021) and Wang and Ong (2017).The former requires a more intensive level of communication, whereas robust approaches require only a limited exchange of information. This by no means represents a dichotomy, these approaches represent two sides of the same problem and the a natural trade-off between performance and ease of computations.…”

Robust Model Predictive Control for Takagi-Sugeno Model With Bounded Disturbances—Pólya Approach

“…Model predictive control (MPC), as a widespread control technique being implemented in a receding horizon fashion, has advantages in constraints handling for multivariable plants, such as distributed MPC [14], industrial hierarchical MPC [15], and stochastic MPC [16]. Usually, at each sampling interval, MPC solves an optimal control problem, with the performance index being associated with the system evolutions over a prediction horizon, subject to physical constraints, where a sequences of control moves are treated as decision variables, but only the first control move among this sequence is implemented on the actuator.…”