H∞ control of dead-time systems based on a transformation

This paper presents a transformation that makes all the robust control problems of dead-time systems able to be solved similarly as in the finite-dimensional situations. With trade-off of the performance, some advantages obtained are: (i) the controller has a quite simple and transparent structure; (ii) there are no any additional hidden modes in the Smith predictor and, hence, there is no additional hidden possibility to destabilize the system; (iii) it can be applied to systems with long dead-time without any difficulty. Hence, the practical significance is obvious.     

Robust stability analysis of Smith predictor-based congestion control algorithms for computer networks

Congestion control is a fundamental building block in packet switching networks such as the Internet due to the fact that communication resources are shared. It has been shown that the plant dynamics is essentially made up of an integrator plus time delay and that a proportional controller plus a Smith predictor defines a simple and effective controller. It has also been shown that the TCP congestion control can be modelled using a Smith predictor plus a proportional controller. Due to the importance of this control structure in the field of data network congestion control, we analyse the robust stability of the closed-loop system in the face of delay uncertainties that are present in data networks due to queuing. In particular, by applying a geometric approach, we derive a bound on the proportional controller gain which is necessary and sufficient to guarantee the closed-loop stability for a given bound on the delay uncertainty.     

Constrained self-adaptive differential evolution based design of robust optimal fixed structure controller

This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence.     

Designing robustly stabilising controllers for LTI spatially distributed systems using coprime factor synthesis

This paper considers the design of feedback controllers for linear, time-invariant, spatially distributed systems in an approach which generalises the H^∞-framework and in particular the H^∞ loop-shaping method. To this end, we introduce a class of spatially distributed system models called finite dimensional, distributed, linear, time-invariant systems. Sensors and actuators are considered to be part of the controller, rather than part of the plant, and thus the controller we wish to design is itself a spatially distributed system. Optimising over placements and shapes of the sensor and actuator spatial distribution functions is an integrated part of the controller design procedure. As an illustrative design example, we present the feedback stabilisation of an electrostatically destabilised, electrically conducting membrane.     

On improving control-loop robustness of model-matching controllers

This note first characterizes the class of all stabilizing controllers for a two-degree-of-Freedom control system which achieve a prescribed achievable transfer function. The characterization is in terms of an arbitrary proper stable transfer function. With this characterization, robust model matching is formulated as a standard H^∞-optimization problem. This means that standard controller designs for a nominal plant, such as linear-quadratic Gaussian ones, can be enhanced to give improved robustness properties using H^∞-design techniques.     

H2/H∞ Control of discrete singularly perturbed systems: the state feedback case

The design of a mixed H₂/H_∞ linear state variable feedback suboptimal controller for a discrete-time singularly perturbed system using reduced order slow and fast subsystems is described. It is shown that the designed controller based on reduced order models and the corresponding performance index both are O(ε) close to those synthesized using the full order system.     

Improved robust H2 and H∞ filtering for uncertain discrete-time systems

This paper is concerned with the robust H₂ and H_∞ filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust H₂ or H_∞ performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters provide extra degrees of freedom in optimizing the guaranteed H₂ or H_∞ performance and lead to a less-conservative design.     

Decentralised robust flow controller design for networks with multiple bottlenecks

Decentralised rate-based flow controller design in multi-bottleneck data-communication networks is considered. An ?^∞ problem is formulated to find decentralised controllers which can be implemented locally at the bottleneck nodes. A suboptimal solution to this problem is found and the implementation of the decentralised controllers is presented. The controllers are robust to time-varying uncertain multiple time-delays in different channels. They also satisfy tracking and weighted fairness requirements. Lower bounds on the actual stability margins are derived and their relation to the design parameters is analysed. A number of simulations are also included to illustrate the time-domain performance of the proposed controllers.     

Delay-dependent robust H∞ control for uncertain systems with a state-delay

A robust H_∞ control for uncertain linear systems with a state-delay is described. Systems with norm-bounded parameter uncertainties are considered and linear memoryless state feedback controllers are obtained. Firstly, a delay-dependent bounded real lemma for systems with a state-delay is presented in terms of linear matrix inequalities (LMIs). By taking a new Lyapunov-Krasovsii functional, neither model transformation nor bounding for cross terms is required to obtain delay-dependent results. Secondly, based on the bounded real lemma obtained, delay-dependent condition for the existence of robust H_∞ control is presented in terms of nonlinear matrix inequalities. In order to solve these nonlinear matrix inequalities, an iterative algorithm involving convex optimization is proposed. Numerical examples show that the proposed methods are much less conservative than existing results.     

Robust switching-type H∞ filter design for linear uncertain systems with time-varying delay

This paper is concerned with the problem of robust H_∞ filter design for a class of linear uncertain systems with time-varying delay. The uncertainty parameters are supposed to be time-varying, unknown, but bounded, which appear affinely in the matrices of the considered system model. Based on linear matrix inequality (LMI) method and switching laws, a new switching-type filter is designed to guarantee the asymptotic stability and H_∞ performance level of the filtering error systems. The key feature is that the new proposed filter parameters are switching between certain fixed gains automatically via the designed switching law. It is shown that the new filter design method is less conservative than the traditional fixed gain filter design method. An example is given to illustrate the validity of the proposed design.     

On pure H reduced-order dynamic controllers: an erratum

There are at least two approaches advocated to obtain a pure H^∞ reduced-order dynamic controller for a given augmented plant. One approach is to eliminate completely the H² aspect from a standard H²/H^∞ setting. A second approach is to equate the H² aspect with the H^∞ aspect in that same setting. This paper invalidates the first approach but affirms the second approach and produces the correct equations resulting therefrom.     

New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI

The problems of relaxed quadratic stability conditions, fuzzy observer designs and H_∞ controller designs for T-S fuzzy systems have been studied. First new stability conditions are obtained by relaxing the stability conditions derived in previous papers. Secondly, new fuzzy observers based on the relaxed stability conditions for the T-S fuzzy systems have been proposed. Thirdly two sufficient LMI conditions, which guarantee the existence of the H_∞ controllers based on fuzzy observers for the T-S fuzzy systems have been proposed. The conditions are not only simple, but also consider the interactions among the fuzzy subsystems. Finally by some examples, using the LMI technique, we show that the regulators, the fuzzy observers and the H_∞ controller designs based on new observers for the T-S fuzzy systems are very practical and efficient.     

Frequency domain solution to delay-type Nehari problem

This paper generalizes the frequency-domain results on the delay-type Nehari problem in the stable case to the unstable case. The solvability condition of the delay-type Nehari problem is formulated in terms of the nonsingularity of three matrices. The optimal value γ_opt is the maximal γ∈(0,∞) such that one of the three matrices becomes singular. All sub-optimal compensators are parameterized in a transparent structure incorporating a modified Smith predictor.     

H robust stabilizability

In this paper, we improve on the results of robust stabilizability obtained by Kimura. We do this in a constructive way by using an H^∞-approach, and exhibit an upper bound for the order of robust controllers.     

The H2-control for jump linear systems: cluster observations of the Markov state

The H₂-norm control problem of discrete-time Markov jump linear systems is addressed in this paper when part of, or the total of the Markov states is not accessible to the controller. The non-observed part of the Markov states is grouped in a number of clusters of observations; the case with a single cluster retrieves the situation when no Markov state is observed. The control action is provided in linear feedback form, which is invariant on each cluster, and this restricted complexity setting is adopted, aiming at computable solutions. We explore a recent result by de Oliveira, Bernussou, and Geromel (Systems Control Lett. 37 (1999) 261) involving an LMI characterization to establish a H₂ solution that is stabilizing in the mean square sense. The novelty of the method is that it can handle in LMI form the situation ranging from no Markov state observation to complete state observation. In addition, when the state observation is complete, the optimal H₂-norm solution is retrieved.     

Robust control for nonlinear systems with structured 2-gain bounded uncertainty

This paper focuses on the problem of robust control design for uncertain nonlinear systems with ₂-gain bounded dynamic uncertainty and periodically time-varying memoryless uncertainty. The robust performance problem is solved via nonlinear ^∞ control with scaling factors. It is shown that the scaling factors can be functions of state variables in contrast with linear robust control.     

Stabilization and H control of symmetric systems: an explicit solution

In this paper we address the H^∞ control analysis, the output feedback stabilization, and the output feedback H^∞ control synthesis problems for state-space symmetric systems. Using a particular solution of the Bounded Real Lemma for an open-loop symmetric system we obtain an explicit expression to compute the H^∞ norm of the system. For the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state-space symmetric systems. For the H^∞ control synthesis problem we derive an explicit expression for the optimally achievable closed-loop H^∞ norm and the optimal control gains. Extension to robust and positive real control of such systems are also examined. These results are obtained from the linear matrix inequality formulations of the stabilization and the H^∞ control synthesis problems using simple matrix algebraic tools.     

An H-minimax approach to the design of robust control systems, part II: All solutions, all-pass form solutions and the ‘best’ solution

We characterize all solutions to a robustness optimization problem as the solutions of a two-parameter interpolation problem. From this characterization it is easy to show that an all-pass form solution always exists as long as a solution exists. We also study the possibility of using non-all-pass form solutions and by introducing other optimization objectives (motivated by improvements in disturbance rejection and robust stability) we search for the 'best' solution.