Robust Continuous-Time Research Articles

Numerical Method for Solving the Robust Continuous-Time Linear Programming Problems

A robust continuous-time linear programming problem is formulated and solved numerically in this paper. The data occurring in the continuous-time linear programming problem are assumed to be uncertain. In this paper, the uncertainty is treated by following the concept of robust optimization, which has been extensively studied recently. We introduce the robust counterpart of the continuous-time linear programming problem. In order to solve this robust counterpart, a discretization problem is formulated and solved to obtain the ϵ -optimal solution. The important contribution of this paper is to locate the error bound between the optimal solution and ϵ -optimal solution.

A Robust Continuous-Time MPC of a DC–DC Boost Converter Interfaced With a Grid-Connected Photovoltaic System

The main function of the DC-DC converter in a grid-connected photovoltaic (PV) system is to regulate the terminal voltage of the PV arrays to ensure delivering the maximum power to the grid. The purpose of this paper is to design and practically implement a robust continuous-time model predictive control (CTMPC) for a dc-dc boost converter, feeding a three-phase inverter of a grid-connected PV system to regulate the PV output voltage. In CTMPC, the system behavior is predicted based on Taylor series expansion, raising concerns about the prediction accuracy in the presence of parametric uncertainty and unknown external disturbances. To overcome this drawback, a disturbance observer is designed and combined with CTMPC to enhance the steady-state performance in the presence of model uncertainty and unknown disturbance such as the PV current, which varies nonlinearly with the operating point. An interesting feature is that the composite controller reduces to a conventional PI controller plus a predictive term that allows further improvement of the dynamic performance over the whole operating range. The effectiveness of the proposed controller was tested numerically and validated experimentally with the consideration of the grid-connected PV inverter system and its controller.

Robust Continuous-Time Matrix Estimation under Dependent Noise Perturbations: Sliding Modes Filtering and LSM with Forgetting

This paper deals with time-varying parameter estimation of stochastic systems under dependent noise perturbations. The filter, which generates this dependent noise from a standard "white noise," is assumed to be partially known (a nominal plant plus a bounded deviation). The considered approach consists of two consecutive steps. At the first step, the application of a sliding-mode-type algorithm is suggested, providing a finite-time equivalence of the original stochastic process with unknown parameters to an auxiliary one. Such an "equivalence" does not cancel the noise effects, but allows one to identify the model in the "regression form" for a sufficiently short time and, simultaneously, to transform the dependent noise, keeping bounded uncertainties as an external unmeasured dynamics. At the second step the least squares method with a scalar forgetting factor (LSMFF) is applied to estimate time-varying parameters of the given model. A convergence zone analysis is presented. A numerical example illustrates the effectiveness of the proposed approach.

A multi-objective control approach for the synthesis of robust digital guidance laws

This paper proposes a new approach for the synthesis of robust digital guidance laws with the objective of achieving stable and accurate missile guidance despite parametric uncertainties in the missile flight control system dynamics, prescribed limits on missile acceleration, and digital implementation at possibly slow sampling rates. The proposed approach is characterized by two consecutive steps. Firstly, a robust continuous-time guidance law is designed using mixed H2-H∞ minimization and pole placement such that the effects of noise and parametric uncertainties are attenuated. To carry out this first step of the approach, missile flight control dynamics are modelled as second-order interval transfer functions, where bounded time-varying parameters characterize the missile flight envelope. Secondly, digital redesign of the robust continuous-time missile control system (including guidance and flight control) is performed by solving an optimal control problem. The proposed global digital redesign strategy results in robust performance for the closed-loop sampled-data missile control system for a wider range of sampling rates than those obtained with currently available approaches and can be readily implemented on commercially available software by following the step-by-step procedure described in the paper. Numerical simulations consisting of a missile pursuing a manoeuvring target, described by the so-called Singer model, demonstrate the effectiveness of the proposed approach.

Robust continuous-time and discrete-time flow control of a dam–river system. (I) Modelling

A distributed parameter linear model is derived from simplified physical equations of one dimensional open channel hydraulics. This linear model relating downstream to upstream flow rates is then identified analytically to a second order transfer function with delay, that can be used for controller synthesis. Analytical formulas for exact sampling with zero and first order holds are also given for the discrete-time case. The modelling error made when considering linear models around different reference discharges in a given set can be evaluated with a bound on multiplicative and on additive uncertainties. These bounds are useful for controller robustness analysis and synthesis.

Robust continuous-time and discrete-time flow control of a dam–river system. (II) Controller design

The paper presents robust design methods for the automatic control of a dam–river system, where the action variable is the upstream flow rate and the controlled variable the downstream flow rate. The system is modeled with a linear model derived analytically from simplified partial derivative equations describing open-channel flow dynamics. Two control methods (pole placement and Smith predictor) are compared in terms of performance and robustness. The pole placement is done on the sampled model, whereas the Smith predictor is based on the continuous model. Robustness is estimated with the use of margins and also with the use of a bound on multiplicative uncertainty taking into account the model errors, due to the nonlinear dynamics of the system. Simulations are carried out on a nonlinear model of the river and performance and robustness of both controllers are compared to the ones of a continuous-time PID controller.

Robust Continuous-Time Asymptotic Tracking and Regulation for Sampled-Data Systems with Structured Parametric Uncertainties

In this paper, the problem of the robust continuous-time (i.e., ripple-free) asymptotic tracking and disturbance rejection for a multivariable sampled-data system is studied, for the case when the available description of the continuous-time plant has a known dependence on some “physical” parameters and possibly only some of the scalar outputs must track corresponding reference signals. The necessary and sufficient conditions for the existence of a hybrid control system for which exponential stability and a continuous-time convergence to zero of the tracking error is guaranteed at least in a neighbourhood of the nominal parameters, are derived here, together with the necessity of a wholly continuous-time internal model of the exogenous signals.

Decentralized Robust Controller for Exponential Stability of Uncertain Systems with Output Feedback

Abstract The paper addresses the problem of design of robust decentralized controllers with output feedback for interconnected linear systems with uncertainties. A new class of robust continuous-time and discrete-time controllers is proposed to guarantee exponential stability of uncertain linear systems without matching conditions. The uncertainties possibly nonlinear can appear both in the subsystems and in the interconnections between them. The proposed algorithm is applied to 6th order system model comprising two subsystems with decentralized controller.

Robust Continuous-Time Indirect Adaptive Control Algorithm

We propose an indirect adaptive control law for continuous-time systems subject to bounded disturbances. The algorithm exploits the least squares covariance matrix properties to cope with the problem of singularities in the control law. Moreover, the disturbance upper bound is estimated which makes unnecessary its explicit knowledge. This estimate is used in a dead-zone introduced in the Least Squares algorithm. Global stability of the closed loop system is proved.