Model-varying predictive control of a nonlinear system

Model Predictive Control (MPC) can be used for nonlinear systems if they are working around an operating point. If the operating point is moved away from the nominal working point the controller is less effective due to model mismatch. This situation can be tackled by using a Model-Varying Predictive Controller (MVPC), which changes its internal model, switching among a set of liner models, according to the working point

Risk adjusted receding horizon control of constrained linear parameter varying systems

In the past few years, control of Linear Parameter Varying Systems (LPV) has been the object of considerable attention, as a way of formalizing the intuitively appealing idea of gain scheduling control for nonlinear systems. However, currently available LPV techniques are both computationally demanding and (potentially) very conservative. In this chapter we propose to address these difficulties by combining Receding Horizon and Control Lyapunov Functions techniques in a risk–adjusted framework. The resulting controllers are guaranteed to stabilize the plant and have computational complexity that increases polynomially, rather than exponentially, with the prediction horizon

Decentralized stabilization of linear time invariant systems subject to actuator saturation

We are concerned here with the stabilization of a linear time invariant system subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers. When there exists no actuator saturation, i.e. when we consider just linear time invariant systems, it is known that global stabilization can be done via decentralized control while using linear time invariant dynamic controllers only if the so-called decentralized fixed modes of it are all in the open left half complex plane

Decentralized stabilization of linear time invariant systems subject to actuator saturation

We are concerned here with the stabilization of a linear time invariant system subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers. When there exists no actuator saturation, i.e. when we consider just linear time invariant systems, it is known that global stabilization can be done via decentralized control while using linear time invariant dynamic controllers only if the so-called decentralized fixed modes of it are all in the open left half complex plane. On the other hand, it is known that for linear time invariant systems subject to actuator saturation, semi-global stabilization can be done via centralized control while using linear time invariant dynamic controllers if and only if the open-loop poles of the linearized model of the given system are in the closed left half complex plane. This chapter establishes that the necessary conditions for semi-global stabilization of linear time invariant systems subject to actuator saturation via decentralized control while using linear time invariant dynamic controllers, are indeed the above two conditions, namely (a) the decentralized fixed modes of the linearized model of the given system are in the open left half complex plane, and (b) the open-loop poles of the linearized model of the given system are in the closed left half complex plane. We conjecture that these two conditions are also sufficient in general. We prove the sufficiency for the case when the linearized model of the given system is open-loop conditionally stable with eigenvalues on the imaginary axis being distinct. Proving the sufficiency is still an open problem for the case when the linearized model of the given system has repeated eigenvalues on the imaginary axis

Risk adjusted receding horizon control of constrained linear parameter varying systems

In the past few years, control of Linear Parameter Varying Systems (LPV) has been the object of considerable attention, as a way of formalizing the intuitively appealing idea of gain scheduling control for nonlinear systems. However, currently available LPV techniques are both computationally demanding and (potentially) very conservative. In this chapter we propose to address these difficulties by combining Receding Horizon and Control Lyapunov Functions techniques in a risk--adjusted framework. The resulting controllers are guaranteed to stabilize the plant and have computational complexity that increases polynomially, rather than exponentially, with the prediction horizon

Anti-windup compensation and the control of input-constrained systems

This chapter introduces the problem of input saturation in systems which are otherwise linear. It is demonstrated how input saturation may cause such systems to exhibit undesirable behaviour. The notion of anti-windup compensators is introduced, followed by a detailed description of a typical anti-windup problem and an effective design procedure. The chapter also emphasizes the role of various nonlinear stability and performance concepts such as Lyapunov stability, sector-boundedness and L2 gain