Optimal decentralized control of dynamic systems

In this paper, several aspects of decentralized control theory applied to dynamic systems are studied. First of all, some classical definitions about matricial functions and new results on gradient calculations are presented. In the following we generalize to matricial problems the method of gradient projection of Rosen. Finally, some aspects of stability, initialization and initial condition independence are studied in detail, and two numerical examples are considered in order to emphasize the advantages of the given procedure: the decentralized Kalman filter and the optimal power-frequency control.     

On the decentralized control of interconnected systems

Recently, it was shown [1] how to reduce the order of the decentralized control problem for interconnected systems by using local dynamic feedback. The analysis was carried out with polynomial matrices. In this letter, these results are reproduced in state space using the Generalized Hessenberg Representation (GHR). This analysis shows how the interaction between the interconnection structure and the local system structure generates the result above. In addition, this analysis leads directly to numerical algorithms.     

Integrity of systems under decentralized integral control

A decentralized controller that maintains closed loop stability, when the individual controllers fail or are taken out of service, provides fault tolerance and flexibility in operation. Recently, necessary and sufficient conditions [Gündes, Kabuli, 2001. IEEE Transactions on Automatic Control, 46(2), 296-301] for the existence of a block decentralized controller with integral action for a system to possess integrity against controller failures were proposed. In this paper, these conditions are equivalently expressed using the well-known notions of Niederlinski index (NI) and block relative gain (BRG). The alternate representation implies that under minor assumptions, the available necessary conditions based on NI and BRG are actually both necessary and sufficient. We also show that confirming the existence of a block decentralized controller with integral action such that the system has integrity is NP-hard.     

On the stabilization of decentralized control systems

This paper considers the problem of stabilizing a linear time-invariant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called "fixed modes," which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given.     

Optimality of decentralized control for large-scale systems

A decentralized control scheme is given for the stabilization of large-scale linear systems composed of a number of controllable subsystems. A class of interconnection structures among subsystems is defined for which the overall system can always be stabilized by local state feedback which is optimal for a quadratic performance index. The resulting closed-loop system has robust stability properties against a wide range of variations in open-loop dynamics. Optimality of the decentralized control law is preserved for a modified performance index under perturbations in interconnections such that the strength of coupling does not increase. The class of decentrally stabilizable large-scale systems presented in this paper is the largest such class hitherto described by the structure of interconnections.     

Optimal decentralized control of large scale systems

This paper presents a new optimized decentralized controller design method for solving the tracking and disturbance rejection problems for large-scale linear time-invariant systems, using only low-order decentralized controllers. To illustrate the type of results which can be obtained using the new optimized decentralized control design method, the control of a large flexible space structure is studied and compared with the standard centralized LQR-observer controller. The order of the resultant decentralized controller is much smaller than that of the standard centralized LQR-observer controller. The proposed controller also has certain fail-safe properties and, in addition, it can be five orders of magnitude more robust than the standard LQR-observer controller based on their real stability radii. The new decentralized controller design method is applied to a large flexible space structure system with 5 inputs and 5 outputs and of order 24.     

Interaction measures for systems under decentralized control

A shortcoming of many of the currently available measures of interactions is their limited theoretical basis. Using the notion of Structured Singular Value (SSV), a new dynamic interaction measure is defined for multivariable systems under feedback with diagonal or block diagonal controllers. This measure can be used not only to predict the stability of decentralized control systems but also to measure the performance loss caused by these control structures. In particular, its steady state value provides a sufficient condition for achieving offset-free performance with the closed loop system. The relationship of this new interaction measure with Rijnsdorp's interaction measure (1965) and Rosenbrock's Direct Nyquist Array (1974) is clarified.     

Spreading the control complexity in decentralized control of interconnected systems

The problem is considered for large scale interconnected systems of designing decentralized dynamic controllers so that the sum of the orders of the local controllers is approximately the system order, while the separate controller orders are more evenly spread than permitted by the procedure of Corfmat and Morse, which generally leads to all memoriless controllers, save one of high complexity. The paper shows that under certain circumstances, it is possible to design dynamic feedback controllers for each channel which introduce stable uncontrollable or unobservable modes to the overall system, thus lowering the effective order of that system. This result is then used to spread the controller complexity.     

Separation of estimation and control for decentralized stochastic control systems

A sufficient condition is given for a separation of estimation and control in decentralized discrete-time stochastic control systems. It is shown that the one-step delay sharing system is a special case satisfying this condition. A counterexample is given, however, to the conjecture that the separation will hold for the more-than-one-step delay sharing systems.     

离散事件系统的混合分散监控

研究了混合信息下的分散监控综合问题.首先提出δ-可观察(hδ-可观察)可控闭语言是(状态部分可观察下)状态反馈综合解存在的充要条件,并由此得到n-联合可观察、可控闭的系统约束是保证混合分散监控器存在的充要条件,进而得到纯分散监控器(控制器)存在的充要条件为n-可观察(n-hδ-可观察)可控闭语言被满足.最后,又通过研究系统约束与混合约束的关系,提出混合分散监控器存在的充分条件是可观察、可控闭语言与可观察可控谓词被满足.     

Stabilizing decentralized model predictive control of nonlinear systems

This note presents a stabilizing decentralized model predictive control (MPC) algorithm for nonlinear discrete time systems. No information is assumed to be exchanged between local control laws. The stability proof relies on the inclusion of a contractive constraint in the formulation of the MPC problem.     

Stabilization of decentralized control systems via time-varying controllers

In the design of decentralized control systems it is well known that the existence of unstable fixed modes prevents us from stabilizing it via linear time-invariant local controllers. In this note, we show that such systems might be stabilizable via time-varying controllers. In particular, a design method using sample and hold is proposed.     

Observability and decentralized control of fuzzy discrete-event systems

Fuzzy discrete-event systems as a generalization of (crisp) discrete-event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete-event system has been modeled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete-event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.     

Limiting interactions in decentralized control of MIMO systems

Despite the closed-loop performance advantages of centralized multivariable controllers, the great majority of industrial process control applications is still based on decentralized controllers. Because of their single loop structure, decentralized controllers cannot suppress the interactions of the plant, which are only taken into account in the controller tuning phase. Therefore, it would be useful in many cases to delimit in some way the undesirable effects of the coupling between inputs and outputs of the closed loop system. A control algorithm to achieve this goal is developed in the paper. The proposal is applicable even to processes with non-minimum phase transmission zeros (provided their off-diagonal transfer functions have their zeros in the left-half-plane). Based on sliding mode attributes, the proposed scheme can be easily added to a previously designed decentralized control system.     

On the decentralized control of interconnected dynamical systems

It is shown that rise fixed modes of an interconnected dynamical system under decentralized control are precisely the uncontrollable and unobservable states of the individual system components. As such, the system can be stabilized by decentralized controllers if and only if its individual system components can be stabilized. Moreover, these conditions are shown to be equivalent to the conditions for stabilizing the system using a global controller.     

Practical stabilization of robotic systems by decentralized control

The practical stability of large-scale robotic systems with variable parameters is considered. The control should ensure the system state to belong to a finite region around the nominal trajectory for various values of parameters. The robotic system is considered as a set of decoupled subsystems each of which corresponds to one degree of freedom. For each decoupled subsystem a local controller is synthesized ensuring the practical stability of free subsystem. Then the practical stability of the coupled global system is analysed for various values of mechanical parameters. This permits the synthesis of decentralized control which provides practical stabilization of robotic systems in given finite regions and for the given set of allowable parameter values. Global control is also introduced. Decentralized control for a manipulation robot with variable payload is synthesized.     

Decentralized blocking zeros and the decentralized strongstabilization problem

This paper is concerned with a new system theoretic concept, decentralized blocking zeros, and its applications in the design of decentralized controllers for linear time-invariant finite-dimensional systems. The concept of decentralized blocking zeros is a generalization of its centralized counterpart to multichannel systems under decentralized control. Decentralized blocking zeros are defined as the common blocking zeros of the main diagonal transfer matrices and various complementary transfer matrices of a given plant. As an application of this concept, we consider the decentralized strong stabilization problem (DSSP) where the objective is to stabilize a plant using a stable decentralized controller. It is shown that a parity interlacing property should be satisfied among the real unstable poles and real unstable decentralized blocking zeros of the plant for the DSSP to be solvable. That parity interlacing property is also sufficient for the solution of the DSSP for a large class of plants satisfying a certain connectivity condition. The DSSP is exploited in the solution of a special decentralized simultaneous stabilization problem, called the decentralized concurrent stabilization problem (DCSP). Various applications of the DCSP in the design of controllers for large-scale systems are also discussed