Andrzej Królikowski

Suboptimal LQG Discrete-Time Control with Amplitude-Constrained Input: Dual Versus Non-Dual Approach

The paper considers a suboptimal solution to the LQG dual and non-dual control problem for discrete-time stochastic systems in the case of amplitude constraint imposed on the control signal. The main dual approach is based on the IPS (Iteration in Policy Space) algorithm proposed in (Bayard DS. IEEE Trans Automat Contr 1991; 9: 1046–1053). The algorithm is essentially a forward method for solving dynamic programming equations using a nested search based on the stochastic approximation technique. An IDC (Innovation Dual Controller) derived in (Milito R, Padilla CS, Padilla RA, Cadorin D. IEEE Trans Automat ContI’ 1982; 1:132–137) has been modified and considered as the second dual approach. As a first non-dual method, the approach consisting in numerical calculation of the probability density fitnction (pdf) of the state estimate (Makila PM. Opt Contr Appl Methods 1982; 3: 337-353) is presented. Next, a suboptimal control method basedon the approach proposed in (Toivonen H. IEEE Trans Automat Contr 1982; 2:246–248) is considered. Finally, a cautious control method is included for comparative analysis. In all algorithms, the truncated second-order filter is applied for joint estimation of the state and unknown system parcuneters. Exalmple of first-order system is simulated in order to compare the performance of control methods. Conclusions yielded from Simulation study are given.

Self-Tuning Control Under Variance and Amplitude Constraints

Abstract A self-tuning control (stc) for ARMAX system in the presence of variance or/and amplitude-constrained input is considered. The control problem is analyzed using the Kuhn-Tucker method. The relation between amplitude and variance constraints is shown when the system is controlled under both constraints. Analysis and computer simulations of second-order system are given.

LQG/LTR Versus Smith Predictor Control for Discrete-time Systems with Delay

A simple LQG control with no control cost is considered for discrete-time systems with input delay. In such case the loop transfer recovery (LTR) effect can be obtained especially for minimum-phase systems. The robustness of this control is analyzed and compared with state prediction control whose robustness stability is formulated via LMI. The robustness with respect to uncertain time-delay is considered including the control systems with Smith predictor-based controllers. Computer simulations of a second-order stable, unstable and nonminimum-phase systems with time-delay are given to illustrate the robustness and performance of the considered controllers.

Adaptive LQG/LTR control; discontinuity issue

An adaptive LQG control with no control cost is considered. In such case the loop transfer recovery (LTR) effect can be obtained. The control problem is handled using discrete-time state-space model and the parameter estimation is performed for corresponding ARMAX model which can be represented in innovation state-space form. Thus the direct estimation of model parameters is possible by means of standard ERLS procedure and the adaptive control is implemented through certainty equivalence principle. In such a situation the problem of solution continuity of Riccati equation can arise for nonminimum-phase systems. Computer simulations of third-order systems modeled by a second-order minimum-phase and nonminimum-phase models are given to illustrate the robustness and performance properties of the adaptive controller, particularly with respect to the modelling error parameter η.

CONTINUOUS-TIME ADAPTIVE LQG/LTR CONTROL

Abstract An adaptive continuous-time LQG control with loop transfer recovery is considered. The control problem is analyzed using state-space model and the parameter estimation problem is implemented for corresponding transfer function model. The direct identification of continuous-time model parameters is possible by means of IDTOOL procedure. Computer simulations of third-order systems modeled by a second-order minimum-phase and nonminimum-phase models are given to illustrate the robustness and performance properties of the adaptive LQG/LTR controller.

Constrained suboptimal dual control algorithms for discrete-time stochastic systems

Abstract Abstract In this paper, a suboptimal solution to the dual control problem for discrete-time stochastic systems under the amplitude-constrained control is considered. The objective of the control is to minimize the two-step quadratic cost function for the problem of tracking the given reference sequence. The presented approach is based on the MIDC (Modified Innovation Dual Controller) derived from an IDC (Innovation Dual Controller) and the TSDSC (Two-stage Dual Suboptimal Control. As a result, a new algorithm, i.e. the two-stage innovation dual control (TSIDC) algorithm is proposed. The standard Kalman filter equations are applied for estimation of the unknown system parameters. Example of second order system is simulated in order to compare the performance of proposed control algorithms. Conclusions yielded from simulation study are given.

LQG control under input variance constraint

In this paper, a variance-constrained LQG control is considered for a plant given by discrete-time ARMAX model. The minimization of constrained quadratic cost is approached by Kalman filter and output feedback methods. The obtained optimization algorithms are simulated for second-order plant model and different constraints.

Discrete-time repetitive control for plants with time delay

Abstract Repetitive control is an effective method to reduce periodic errors with a known period in various practical control systems performing repetitive tasks. The paper presents a comparison of main repetitive control structures putting an emphasis on tracking and disturbance rejection properties of repetitive control systems for plants with uncertain time delay.

Modeling and Adaptive Control for a Two-Link Flexible Manipulator

Abstract Dynamic nonlinear model of an experimental two-link flexible manipulator is presented and simulated in order to determine its frequency properties. An adaptive control algorithm based on the presented model is given along with the simulation results.

Discussion on: ‘Suboptimal LQG Discrete-Time Control with Amplitude Constrained Input’ by A. Królikowski

(a) iteration in policy space (lPS); (b) modified innovation dual control (MIDC) onestep-ahead dual. Three non-dual control methods are also considered; (c) distribution certainty equivalence (the control is a linear feedback of the estimated state subject to saturation, with an averaging carried out over this estimate according to an approximate stationary pdf); (d) a heuristic certainty equivalence version of the control proposed by Toivonen (linear quadratic control subject to saturation), i.e., with the parameter estimates used as if they were the true values; (e) a cautious control (CAUT) which accounts with a one step horizon for the current parameter uncertainties.