Optimal Control Of Large-scale Systems Research Articles

A Noise History Decomposition Approach for Decentralized Optimal Control of Large-Scale Systems Defined Over a Weakly Connected Graph

This article investigates the decentralized optimal linear quadratic regulation (LQR) control for large-scale systems. The large-scale system is defined over a weakly connected graph. Assume that the information is transmitted along the edges in the graph, and one sampling period is required for the information to travel across an edge. Under the above setup, the LQR control problem for the strongly connected graph case has been fully solved. However, for the weakly connected graph case, the existing results fail. In this article, a new decomposition approach for noise history is proposed. Then, the LQR control problem of large-scale systems defined over a weakly connected graph can be well solved. In addition, the decentralized realization of the control input is derived based on the decentralized information hierarchy graph (DIHG). The DIHG construction algorithm is also provided. Finally, the effectiveness of the developed design scheme is illustrated by a numerical example.

A Hierarchical MPC Scheme for Ensembles of Hammerstein Systems

Hierarchical control approaches have been one of the elective methods for the optimal control of large-scale systems in the last decades. In (Petzke et al., 2018) we presented a multirate hierarchical MPC scheme for linear systems, with remarkable flexibility and scalability properties. In this paper we extend the former approach to ensembles of Hammerstein systems and we complement the method by proposing a suitable high-level optimizer. The theoretical properties are discussed in the light of the theoretical properties of the former method. Lastly, an example case study is presented to show the effectiveness of the proposed method.

Sparsity preserving optimal control of discretized PDE systems

We focus on the problem of optimal control of large-scale systems whose models are obtained by discretization of partial differential equations using the Finite Element (FE) or Finite Difference (FD) methods. The motivation for studying this pressing problem originates from the fact that the classical numerical tools used to solve low-dimensional optimal control problems are computationally infeasible for large-scale systems. Furthermore, although the matrices of large-scale FE or FD models are usually sparse banded or highly structured, the optimal control solution computed using the classical methods is dense and unstructured. Consequently, it is not suitable for efficient centralized and distributed real-time implementations. We show that the a priori (sparsity) patterns of the exact solutions of the generalized Lyapunov equations for FE and FD models are banded matrices. The a priori pattern predicts the dominant non-zero entries of the exact solution. We furthermore show that for well-conditioned problems, the a priori patterns are not only banded but also sparse matrices. On the basis of these results, we develop two computationally efficient methods for computing sparse approximate solutions of generalized Lyapunov equations. Using these two methods and the inexact Newton method, we show that the solution of the generalized Riccati equation can be approximated by a banded matrix. This enables us to develop a novel computationally efficient optimal control approach that is able to preserve the sparsity of the control law. We perform extensive numerical experiments that demonstrate the effectiveness of our approach.

Fuzzy-based interaction prediction approach for hierarchical control of large-scale systems

This paper presents a fuzzy-based interaction prediction approach (F-IPA) for two-level optimal control of large-scale systems. The design procedure uses a decomposition/coordination framework of hierarchical structures. At the first level, the system is decomposed into subsystems for which subproblems are formed. At the second level, a fuzzy coordinator is used to predict the coordination parameters needed to coordinate the solutions of the first level subproblems. The fuzzy coordinator uses a critic vector to evaluate its performance and learn its parameters by minimizing an energy function. The proposed control scheme is implemented on a two-degrees-of-freedom (2DOF) model of robot manipulator with parallel links and two inverted pendulums on cars. Simulation results are obtained and compared with the gradient-based interaction prediction approach (G-IPA) and a centralized optimization.

Decentralized Adaptive Optimal Control of Large-Scale Systems With Application to Power Systems

This paper studies the optimal control problem for large-scale systems with unknown parameters and dynamics. By using robust adaptive dynamic programming (RADP) method, a decentralized optimal control design is given for large-scale systems with unmatched uncertainties. The convergence of the proposed RADP algorithm and the asymptotic stability of the closed-loop large-scale system are studied rigorously. Finally, a numerical example of a large-scale power system is adopted to illustrate the effectiveness of the obtained algorithm.

Robust optimal control for large-scale systems with state delay

Optimal control of large-scale uncertain dynamic systems with time delays in states is considered in this paper. For this purpose, a two-level strategy is proposed to decompose the large-scale system into several interconnected subsystems at the first level. Then optimal control inputs are obtained by minimization of convex performance indices in presence of uncertainties, in the form of states and interactions feedback. The solution is achieved by bounded data uncertainty problems, where the uncertainties are only needed to be bounded and it is not required to satisfy the so-called ‘matching conditions’. At the second level, a simple substitution-type interaction prediction method is used to update the interaction parameters between subsystems. An iterative two-level algorithm is proposed to coordinate their solutions and achieve the optimal solution of the overall large-scale system. Applicability and performance of the proposed algorithm is shown through simulation of a two coupled inverted pendulums.

Optimal control for large-scale systems: a recursive approach

A recursive fixed-point-type method is presented for the study of the optimal control problem of large-scale systems. The control is obtained by decomposition of the system to ‘e coupled’ subsystems so that only low-order systems are involved in algebraic computations. It is shown that the developed reduced-order parallel algorithms converge to the desired solution with the rate O(e). Owing to its recursive nature, the presented method produces a considerable saving of computation. An illustrative numerical example is given to verify the proposed approach.