The discrete time minimum entropy H∞H_\infty control problem

This paper completely solves the discrete time minimum entropy control problem. It is shown that in discrete time the central controller has the additional interpretation as the controller which minimizes a minimum entropy criterion. This is completely analogous to the continuous time. However, although the $H_\infty$ control problems for discrete and continuous time can be connected via the bilinear transform, it is shown that this is not the case for the corresponding minimum entropy control problems and hence the bilinear transform does not connect the central controllers in continuous and discrete time. Keywords: $H_\infty$ control, algebraic Riccati equation, discrete time systems, minimum entropy, bilinear transform

Squaring down and the problems of almost zeros for continuous-time systems

In this paper we construct precompensators which square down a system such that the resulting square system has the same unstable zeros and system gains We derive the mlmmal gain of the precompensator to achieve such a square system If the gain of this precompensator Is too large then we derive an explicit trade-off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the syste

Perspectives of data-driven LPV modeling of high-purity distillation columns

Abstract—This paper investigates data-driven, Linear- Parameter-Varying (LPV) modeling of a high-purity distillation column. Two LPV modeling approaches are studied: a local approach, corresponding to the interpolation of Linear Time- Invariant (LTI) models identified at steady-state purity levels, and a global Least-Square Support Vector Machine (LSSVM) approach which offers non-parametric estimation of the system w.r.t. data with varying operating conditions. In an extensive simulation study, it is observed that the global LSSVM approach outperforms the local methodology in capturing the dynamics of the high-purity distillation column under study. The simulation results suggest that the global LS-SVM approach provides a reliable modeling tool under realistic noise conditions

Asymptotic characteristics of Toeplitz matrix in SISO model predictive control

The singular value decomposition (SVD) of the Toeplitz matrix in the quadratic performance index of Model Predictive Control (MPC) is studied. It was shown in Rojas et al. (2003, 2004) that for sufficiently long prediction horizons, the eigenvalues of the Hessian matrix converge to the energy density spectrum of the associated system seen by the performance index. In this paper, we extend that work and show that the left and right singular vectors of the Toeplitz matrix provide the phase information of the associated system for sufficiently long prediction and control horizons. A SISO system is used to illustrate the method

Asymptotic behaviour of Toeplitz matrix in multi-input multi-output model predictive control

The singular value decomposition of (SVD) of the Toeplitz matrix in the quadratic performance index of Model Predictive Control (MPC) is studied. The underlying goal is to find connection between the frequency domain information and the finite time optimal control and use this connection as a basis for stability, robust performance analysis and tuning of the dynamic MPC criterion. In a recent work by the authors, it was shown that the singular value decomposition of the Toeplitz matrix provides gain and phase information of the associated system for sufficiently long prediction and control horizons. This work is extended to MIMO case and is shown that singular value decomposition of the Toeplitz matrix can be used for stability analysis of closed loop system

Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller