Jan Štecha

Linearization: Students Forget the Operating Point

Linearization is a standard part of modeling and control design theory for a class of nonlinear dynamical systems taught in basic undergraduate courses. Although linearization is a straight-line methodology, it is not applied correctly by many students since they often forget to keep the operating point in mind. This paper explains the topic and suggests a way to improve the teaching of the methodology in control courses. The idea is presented on a model of an inverted pendulum on a cart-a classical laboratory model used in the control theory education process.

LQ and dead beat control combination from the set of stabilizing controllers

Stability is the first demand of the feedback control design. The parametrization of all stabilizing controllers is standard theory. The stabilizing controller has some free parameters which can be used for further optimization. Linear Quadratic (LQ) control and Dead Beat control are standard algorithms for optimal control of discrete time models of real systems. The dead beat control results in very large input signals which are not realizable. The LQ control is widely used, because enables to tune the criterion to our requirements. In this paper the combination of both tuning algorithms is presented. The dead beat control algorithm has a unique solution. To enlarge number of steps gives us free parameters which can be used for the optimization of LQ criterion.

LQ/LQG controller for parallel models

Abstract The paper presents LQ/LQG optimal controller based on a set of parallel models with given probabilities of individual models (mixture distribution). Both state feedback LQ controller (in case of measurable state) and output feedback LQG controller are described.

One-step active control strategy as approximation of dual control

Abstract Stochastic adaptive control gives a possibility to deal with uncertainties in system descriptions. In contrast to other robust methods, it uses probabilistic description of uncertain system parameters and consequently, stochastic optimization methods are used to design the controller. It also uses identification methods to improve the system model and thus further improve overall performance. In stochastic adaptive control, the controller that achieves required control performance and keeps gathering information about the system at the same time, is referred to as a controller with dual properties. As the optimal dual controller is computationally intractable, approximations of the optimal problem are searched. In this paper we propose a control strategy for ARX systems with dual properties. This active control strategy is based on the well known cautious strategy, but takes the quality of identification in one step ahead into consideration. This strategy shows how to improve control performance mainly in cases when the initial uncertainty in system parameters is large.

Tree Structures for Identification with Alternative Models 1

Abstract An approach to the detection of changes in parameters of a dynamical system and measurement errors for a finite number of models of possible parameter changes and measurements is presented.

Stochastic maximum principle

Abstract The Pontrjagin maximum principle solves the problem of optimal control of a continuous deterministic system. The discrete maximum principle solves the problem of optimal control of a discrete-time deterministic system. The maximum principle changes the problem of optimal control to a two point boundary value problem which can be completely solved only in special tasks. It was probably the reason that the maximum principle is not in favor this time. Optimal control of stochastic systems or even systems with probabilistic parameters is usually derived using stochastic dynamic programming. In the paper an alternative approach based on a stochastic modification of the maximum principle is presented, both for continuous and discrete-time systems. Cautious and certainty equivalent optimal control strategies are then derived using this method and the results are consistent with those achieved by stochastic dynamic programming.

Mathematical Models for Hotel Yield Management

Effective management practices in the tourism and hotel area have seldom been more important than at the present time. Pricing decisions cannot be taken without serious thought. The key idea is to formulate a pricing strategy of a provider as a sequential decision problem, which can be transformed into an optimal control problem. The yield management can therefore be understood as a new application field for the model based prediction control (MPC). It can be shown that the hotel yield management problem can be cast as a MPC feedback control problem. The article presents convenient demand modeling along with final problem formulation that is inspired by MPC. Final formulation integrates various economy phenomena (service substitution, overbooking) and produces quick feasible solution that is based on quadratic programming algorithm.

System parameter estimation using total P-norm minimization

Abstract Real time system parameter estimation from the set of input-output data is usually solved by the quadratic norm minimization of system equations errors – known as least squares (LS). But measurement errors are also in the data matrix and so it is necessary to use a modification known as total least squares (TLS) or mixed LS and TLS. Instead of quadratic norm minimization other p-norms are used, for 1 ≥ p ≥ 2. In the article new method is described named Total p-norm and Mixed total p-norm which is the analog to TLS and mixed LS and TLS method in the quadratic case. The goal of the paper is to develop the method and to compare a set of parameter estimations of ARX model where each estimation is obtained by minimizing total p-norm (1 ≥ p ≥ 2). Total p-norm and mixed total p-norm approach is used when errors are also in data matrix. If the measurement of the system output is damaged by some outliers described method gives better results than standard TLS or mixed LS and TLS approach.

Chapter 23 – Alternative Models of Adaptive and Near-Rational Expectations — Classification by Bootstrap Filter

Publisher Summary This chapter examines the alternative models of adaptive and near-rational expectations-classification by Bootstrap filter. The problem of deciding between alternative hypotheses is common. There may be two or more theories on a model background or parameter values and the data should determine which alternative is the most plausible. In case one of these models is nonlinear, the Monte Carlo approach should be used instead of linear methods. Such an approach is employed for classifying expectation formation within augmented Phillips curve. It is found that before the prediction phase the importance resampling is performed. It makes it no longer necessary to calculate with sample weights, because they are all equal. The other advantage is that there are no samples with small weights. Some samples with greater weight are selected two or more times while some samples are not selected at all. The prediction step is realized according to the state space model of the system. The probability of each model is computed based on the data. Such an approach is used for the classification of alternative economic models of expectation formation.

Alternative Models of Adaptive and Near-Rational Expectations — Classification by Bootstrap Filter

Abstract The problem of deciding between alternative hypotheses is common. There may exist two or more theories on a model background or parameter values and the data should determine which alternative is the most plausible. In case one of these models is nonlinear, the Monte Carlo approach should be used instead of linear methods. Such an approach is employed for classifying expectation formation within augmented Phillips curve.