Editorial

Abstract

Optimality of performance in the presence of uncertainty and constraints constitutes a difficult yet vitally important problem in control. It is in this context that model predictive control (MPC) came into prominence, with its ability to take explicit account of constraints while keeping computational complexity to manageable levels through receding horizon implementation. Over the past 30 years the field has received much research attention and has undergone major development. With the emergence of a plethora of theoretical results and the derivation of numerous algorithms of ever increasing sophistication, predictive control of both linear and nonlinear systems is now reaching a state of maturity, and there is convergence to a consensus. Many areas remain in need of development; however, and it is the intention of this Special Issue to highlight some of these areas, and to present some preliminary work that we hope will both inform the readership and inspire future work in the area. Despite the large number of reported applications of linear predictive control, there is still a dearth of significant advances demonstrating the advantages offered by predictive algorithms in the control of nonlinear systems. Several contributing factors exist here, the most significant of which are the lack of reliable/useful models, the presence of model uncertainty (which may be of a stochastic nature), and the high complexity of computation. This Special Issue offers contributions that address all of these issues. In particular, the first four papers, which are primarily concerned with applications, propose models and algorithms that prove useful in some new and exciting real life problems. Namely: the alleviation of circadian-related disorders (Bagheri, Stelling and Doyle), control of direct torque drive electric motors in a hybrid mixed logical dynamical formulation of inverter switching (Papafotiou, Geyer and Morari), control of power generating kites under variable wind conditions (Ilzhöfer, Houska and Diehl), and stochastic control of thin-film deposition batch process (Nagy and Algöwer). All of these papers are concerned with issues of robustness, and evidence is given (through simulated responses) of satisfactory performance. Computational complexity is likewise addressed by all of these papers, and a range of tools is explored in the interests of expediting practical implementation: genetic algorithms, mixed-integer linear programming with multiple-rate predictions, multiple shooting, and sparse interior point algorithms. There is also concern for stochastic uncertainty, with one of the papers proposing a performance index that is a weighted mix of approximate expected values and variances. Striking the correct balance between efficacy of application and theoretical rigour (especially in respect of satisfaction of constraints, guarantees of feasibility, and a well-defined evaluation of robustness) is always difficult to achieve. It is to be hoped that the contributions in this issue will provide the impetus for further development of these topics and lead to reports of the application of NMPC to actual (as opposed to simulated) processes. The remaining three papers in the issue are of a theoretical nature, but their concerns overlap with those of the first four papers. Sznaier, Lagoa and Ozay consider the use of linear parameter varying models as a means of formalizing the intuitively appealing idea of gain scheduling for nonlinear systems. A stochastic approximation algorithm with guaranteed convergence is proposed, and, despite the use of closed-loop strategies that cater for worst-case performance, appropriate use of linear matrix inequalities ensures that computational complexity grows only polynomially (rather than exponentially). Computational issues are also the concern of the paper by Guay and Dehaan, which examines robustness issues associated with non-local search methods in continuous time MPC and demonstrates a framework for robustly incorporating these approaches in a real-time setting. Finally, the paper by Raimondo, Magni and Scattolini develops a stabilizing decentralized MPC scheme for discrete time nonlinear systems, whose subsystems are locally controlled by predictive controllers that guarantee input-to-state stability. Treating the effects of interconnections as perturbations, the paper establishes the input-to-state stability of the overall system. In conclusion, the Special Issue covers a range of issues and presents some novel contributions, both in respect of applications and developments in control theory. In addition to reporting some effective solutions to difficult problems, the papers presented in this issue also highlight the need for further work, in particular: application of NMPC to actual processes, reduction in computation so as to enable implementation for fast sampling processes, derivation of non-conservative bounds on robust performance, robust guarantees of feasibility and constraint satisfaction for systems subject to stochastic uncertainty. No doubt, with the intense interest in predictive control, solutions to some of these remaining questions will become available in the very near future. Past experience shows, however, that new questions will arise as soon as such solutions are discovered. One certainty is that the future is bright for both the theory and the practice of MPC.