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This paper is concerned with the optimal static distributed control problem for linear discrete-time deterministic and stochastic systems. The objective is to design a stabilizing static distributed controller whose performance is close to that of the optimal centralized controller. To this end, we first consider deterministic systems, where the initial state is either given or belongs to a known bounded region. Given an arbitrary centralized controller, we derive a condition under which there exists a distributed controller that generates input and state trajectories close to their counterparts in the centralized closed-loop system. This condition for the design of a distributed controller is translated into an optimization problem, where the optimal objective value of this problem quantifies the closeness of the designed distributed and given centralized control systems. The results are then extended to stochastic systems that are subject to input disturbance and measurement noise. The proposed optimization problem has a closed-form solution (explicit formula) and can be efficiently solved for large-scale systems. The mathematical framework developed in this paper is utilized to design a near-globally optimal distributed controller based on the optimal centralized controller, and strong theoretical lower bounds on the global optimality guarantee of the obtained distributed controller are derived. We show that if the optimal objective value of the proposed convex program is sufficiently small, the designed controller is stabilizing and nearly globally optimal. To illustrate the results, case studies on aircraft formation and frequency control of power systems are offered. [ABSTRACT FROM AUTHOR]

In this paper, we propose decentralized control of networks of discrete-time nonlinear control systems, enforcing complex specifications expressed in terms of regular languages, within any desired accuracy. As discussed in the paper, regular languages are useful to model a rather wide variety of complex specifications for control systems. The design of decentralized controllers is based on formal methods and, in particular, on the use of discrete abstractions. Efficient synthesis of such controllers is derived by resorting to on-the-fly algorithmic techniques that also allow the use of parallel computing architectures. Advantages and disadvantages of the decentralized approach over a centralized one, also in terms of computational complexity, are discussed. An illustrative example is presented, which shows the applicability and effectiveness of the results proposed. [ABSTRACT FROM AUTHOR]

This paper considers centralized and decentralized control problems for partially-observed discrete event systems where sensor readings are assumed to be costly for reasons of bandwidth, energy, or security. The supervisory controllers, or agents, dynamically request sensors readings as needed to observe the trajectories of the system and correctly implement the given feedback control law. Thus, each sensor may be turned on/off several times along a given system trajectory. Different policies for dynamic sensor activation can be used by the agents. A set of policies is said to be minimal if any strictly less activation prevents the correct implementation of the control law. A systematic formulation of the dynamic sensor activation problem is proposed and its solution developed when the solution space is restricted to the set of transitions of a given automaton model of the system. Two algorithms that compute minimal sensor activation policies are presented, one for ensuring observability and the other for ensuring coobservability; observability and coobservability are key properties that arise in the solution of supervisory control problems for centralized and decentralized discrete event systems. These algorithms are of polynomial complexity in both the number of states and the number of events of the system. [ABSTRACT FROM PUBLISHER]

Disturbance decoupling problem (DDP) of Boolean control networks is considered. Using semi-tensor product of matrices and the matrix expression of logical functions, a working procedure is proposed to solve the problem. This procedure consists of two key design steps. First, how to convert a system into an output-friendly coordinate frame. An algorithm is provided to calculate the output-friendly subspaces. Secondly, it was shown how to find proper controllers to solve the problem if it is solvable. A state variable separation form is introduced to guide the design of controllers. Based on the design technique, necessary and sufficient conditions are obtained for the solvability of DDP. [ABSTRACT FROM AUTHOR]