Model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints

Robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative. This paper overcomes these issues through an augmented autonomous prediction formulation, and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance, namely invariance with probability p.     

On partitioned controllability of switched linear systems

When a switched linear system is not completely controllable, the controllability subspace is not enough to describe the controllability of the system over whole state space. In this case the state space can be divided into two or three control-invariant sub-manifolds, which form a control-related partition of the state space. This paper investigates when each component is a controllable sub-manifold. First, we consider when a sub-manifold is controllable for no control input case. Then the results are used to produce a necessary and sufficient condition assuring the controllability of the partitioned control-invariant sub-manifolds of a class of switched linear systems. An example is given to demonstrate the effectiveness of the results.     

Multi-frequency disturbance rejection via blending control technique for hard disk drives

This paper is concerned with the rejection of multiple narrowband disturbances in hard disk drives (HDDs). Inspired by a control blending idea, the multi-frequency disturbance rejection is formulated as a blending control problem. Each disturbance rejection is accomplished by using the H₂ optimal control method. Based on all H₂ optimal controllers, the blending technique is applied to yield a single controller which is capable of achieving rejection of all disturbances. Rejections of two and three disturbances for a 1.8-inch HDD VCM actuator are taken as application examples in the paper. Simulation and experimental results show that the ultimate controller results in a simultaneous attenuation of disturbances with frequencies higher or lower than the closed-loop system bandwidth. Moreover, the method turns out to be able to lift phase and thus prevent phase margin loss when it is used to deal with disturbances near bandwidth.     

On the addition of integral action to port-controlled Hamiltonian systems

A technique that provides closed loop integral action depending on the passive outputs of port-controlled Hamiltonian systems is already available. This paper addresses a new method that allows us to add integral action also on system variables having relative degree higher than one, while still preserving the Hamiltonian form and, thus, closed loop stability. The new approach is applied to design speed regulation controllers for the permanent magnet synchronous motor. Closed loop stability and asymptotic rejection of unknown piecewise constant load torques are formally proved. This theoretically predicted control system performance is illustrated via simulation experiments, which also show that the properties hold under parameter uncertainties. This is in line with the usual practice of including integral action in a controller with the aim of improving its closed loop robustness. The fact that the method enhances the range of possible integral actions in the controller, enriched with this robustness property, allows us to assess it as a practically important complement to the well-known interconnection and damping assignment techniques developed in the framework of port-controlled Hamiltonian systems.     

Linear offset-free Model Predictive Control

This work addresses the problem of offset-free Model Predictive Control (MPC) when tracking an asymptotically constant reference. In the first part, compact and intuitive conditions for offset-free MPC control are introduced by using the arguments of the internal model principle. In the second part, we study the case where the number of measured variables is larger than the number of tracked variables. The plant model is augmented only by as many states as there are tracked variables, and an algorithm which guarantees offset-free tracking is presented. In the last part, offset-free tracking properties for special implementations of MPC schemes are briefly discussed.     

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

Optimal dynamic advertising with an adverse exogenous effect on brand goodwill

We propose the model of a firm that advertises a product in a homogeneous market, where a constant exogenous interference is present. Using the framework of Nerlove and Arrow’s advertising model, we assume that the interference acts additively on goodwill production as a negative term. Hence, we allow that the goodwill may become negative and we associate a zero demand with negative goodwill values. We consider a piecewise linear demand function and formulate a nonsmooth optimal-control problem with an infinite horizon. We obtain that an optimal advertising policy exists and takes one of two forms: either a positive and constant advertising effort, or a decreasing effort starting from a positive level and eventually reaching the zero value at a finite exit time. In the former scenario, the demand is always positive and the firm stays in the market in the long run; in the latter, the demand becomes zero in the short run, and afterward, the firm goes out of business. In both cases we have an explicit representation of the optimal control, which is obtained through the study of an auxiliary smooth optimal-control problem. It is interesting that the fundamental choice between staying in the market and going out of business at some time depends both on the interference level and on the initial goodwill level.     

A discrete delay decomposition approach to stability of linear retarded and neutral systems

This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov-Krasovskii functionals. These Lyapunov-Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov-Krasovskii functionals employed in [Han, Q.-L. (2005a). Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41, 2171-2176; Han, Q.-L. (2005b). A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469-475]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov-Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in Han (2005a) and Han (2005b) cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.     

Observer-based networked control for continuous-time systems with random sensor delays

This paper is concerned with the networked control system design for continuous-time systems with random measurement, where the measurement channel is assumed to subject to random sensor delay. A design scheme for the observer-based output feedback controller is proposed to render the closed-loop networked system exponentially mean-square stable with H_∞ performance requirement. The technique employed is based on appropriate delay systems approach combined with a matrix variable decoupling technique. The design method is fulfilled through solving linear matrix inequalities. A numerical example is used to verify the effectiveness and the merits of the present results.     

Barrier Lyapunov Functions for the control of output-constrained nonlinear systems

In this paper, we present control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint. To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we ensure that those limits are not transgressed. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output. Furthermore, we explore the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. We also compare our control with one that is based on a Quadratic Lyapunov Function, and we show that our control requires less restrictive initial conditions. A numerical example is provided to illustrate the performance of the proposed control.