Solution to the inverse regulator problem for discrete-time systems

A complete solution is given for the inverse problem of LQ optimal regulators for the discrete-time multi-input case. The Kalman equation for discrete-time systems is derived to characterize the optimal regulators. It is then shown that this equation holds for some quadratic weighting if and only if the feedback satisfies a condition corresponding to the circle criterion for continuous-time systems. The optimality criterion given here consists of this condition and an additional condition to ensure detectability. An example is given to illustrate the results.     

Output consensus for high-order linear time-invariant swarm systems

Output consensus analysis and design problems of high-order linear time-invariant swarm systems are investigated. First, an output consensus subspace and a complement output consensus subspace are introduced. By output projection onto the two subspaces and the partial stability theory, a necessary and sufficient condition for output consensus is presented, and an explicit expression of the output consensus function, which is jointly determined by the interaction topology and initial states of all agents, is given. Especially, it is shown that the output consensus function is completely determined by initial states of all agents if the interaction topology is balanced. Then, an approach to determine gain matrices in consensus protocols of swarm systems is proposed, which has less calculation complexity. Finally, a numerical example is shown to demonstrate theoretical results.     

Output regulation problem for discrete-time linear time-delay systems by output feedback control

In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuous linear time-delay systems.     

Output deadbeat control discrete-time multivariate systems

An algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback. The central part of the algorithm is the construction of the nonunique state-cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties     

离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

Graphs,closability, and causality of linear time-invariant discrete-time systems

In this paper a linear, time-invariant, discrete-time system is considered by regarding it as an (unbounded) operator on 2(N), 2(Z), CN or CZ. The graphs of closed systems are characterized and properties such as causality and closability of systems are studied. It is shown that the closure of a causal, closable system on 2(N), CN and CZ is again causal, whereas this is in general not the case for systems on 2(Z). Necessary and sufficient conditions which guarantee that this property hold for systems on 2(Z) are given. Many of the results extend without change to the continuous-time case.     

Output regulator problem of a nuclear reactor system

A control problem of distributed reactor systems is investigated. After kinetic equations are expanded into Kaplan modes, the output regulator with structural stability is applied to the spatial mode system. In particular, the fundamental mode is regarded as an exogeneous input signal to the spatial control system due to a variation of control rods from the power control system. The output to be regulated is the neutron flux deviation from the equilibrium value at some specified points where the fuels in burn-up are located. Some numerical simulation results are presented to show the effectiveness of the proposed method.