Probability-constrained analysis, filtering and control

Rather than requiring the objectives of system performance to be met accurately, it is quite common for practical systems design to have the individual performance objective being described in terms of the desired probability of attaining that objective. In this context, constrained probability analysis, filtering and control (CPAFC) problems are of significant engineering importance, mainly for two reasons: (1) it is almost impossible to ensure that certain performances are achieved with probability 1 because of uncontrolled external forces and unavoidable modelling errors; and (2) in some cases, it is satisfactory if certain performances are achieved with an acceptable probability. CPAFC problems can find applications in various engineering applications. For example, in the control of large space structures, the vibration level at multiple points on the structure must be kept within specified bounds with certain guaranteed probability. Other examples include the paper making control problem, telescope pointing problem, robot arm pointing problem, spacecraft intercept problem and meantime-between-failures control problem. These kinds of engineering problems place increasing demands on systems analysis and design because the problems under consideration generally involve multiple objectives, that is, the probability restrictions on performance requirements of the system outputs. Traditional system design techniques, such as LQG, H1 and L1 designs, do not give a direct solution to the above CPAFC problems. For instance, LQG controllers minimise a linear quadratic performance index, which is actually the expectation (or average) of the performance evaluated by means of theH2 norm, leading to a calculable output variance. As such, LQG design lacks guaranteed probability constraints with respect to individual system outputs or performances. It should be pointed out that, recently, there has been a growing research interest in studying conventional filtering and control problems within a probabilistic framework by using a variety of optimisation approaches. The CPAFC has already become an ideal research area for control engineers, mathematicians, and computer scientists to manage, analyse, interpret and synthesise probabilistic information from realworld systems under stochastic disturbances. Sophisticated system theories and computing algorithms have been exploited or emerged in the general area of CPAFC, such as analysis and control of probability density functions, analysis and control with randomised algorithms, probability-constrained predictive control, as well as networked system analysis with probability constraints. This special issue aims to bring together the latest approaches to understanding filtering and control for complex systems with probabilistic performance constraints. Topics include, but are not limited to the following aspects: (1) systems analysis with probability constraints; (2) probabilistic parameter identification of stochastic systems; (3) robustness with probability constraints; (4) methods and algorithms for randomised dynamics analysis; and (5) probabilityconstrained estimation, filtering and control for networked control systems. We have solicited submissions to this special issue from electrical engineers, control engineers, mathematicians and computer scientists. After a rigorous peer review process, 16 papers have been selected that provide overviews, solutions or early promises, to manage, analyse and interpret dynamical behaviours of complex systems with probability constraints. These papers cover both the practical and theoretical aspects of control and filtering with probabilistic performance constraints in the broad areas of dynamical systems, mathematics, statistics, operational research and engineering. The standard robust analysis and control assures (only) a performance bound over the uncertainty region, which provides no information regarding the performance variation (or dispersion) over the uncertainty region. In a probabilistic robust performance context, it might be interesting and useful to address, for example, the ‘mean’ (to be defined) performance over the uncertainty region. If a better mean and a better bound are contradicting goals, one may sometimes be prepared to accept a slightly worse performance bound in order to obtain significantly better ‘mean’ performance. In the article, ‘Polytopic bestmean H1 performance analysis’ by Boyarski, the probabilistic versions of standard polytopic convex robust H1 analysis and state-feedback synthesis problems are studied for asymptotically stable infinite-horizon linear systems. This article focuses on the performance distribution over the uncertainty region (rather than just on the performance bound, as is customary in current robust control), and on