Parameter bounds for discrete-time Hammerstein models with bounded output errors

In this note, we present a two-stage procedure for deriving parameters bounds in Hammerstein models when the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear part are tightly bounded. Then, for a given input transient sequence we evaluate tight bounds on the unmeasurable inner signal which, together with noisy output measurements are used for bounding the parameters of the linear dynamic block.     

Parameter bounds evaluation of Wiener models with noninvertible polynomial nonlinearities

In this paper a three stage procedure is presented for deriving parameters bounds of SISO Wiener models when the nonlinear block is modeled by a possibly noninvertible polynomial and the output measurement errors are bounded. First, using steady-state input-output data, parameters of the nonlinear part are bounded by a tight orthotope. Then, given the estimated uncertain nonlinearity and the output measurements collected exciting the system with an input dynamic signal, bounds on the unmeasurable inner signal are computed. Finally, such bounds, together with noisy output measurements, are used for bounding the parameters of the linear block.     

A high-gain scaling technique for adaptive output feedback control of feedforward systems

In this note, we propose an adaptive output feedback control design technique for feedforward systems based on our recent results on dynamic high-gain scaling techniques for controller design for strict-feedback systems. The system is allowed to contain uncertain functions of all the states and the input as long as the uncertainties satisfy certain bounds. Unknown parameters are allowed in the bounds assumed on the uncertain functions. If the uncertain functions involve the input, then the output-dependent functions in the bounds on the uncertain functions need to be polynomially bounded. It is also shown that if the uncertain functions can be bounded by a function independent of the input, then the polynomial boundedness requirement can be relaxed. The designed controllers have a very simple structure being essentially a linear feedback with state-dependent dynamic gains and do not involve any saturations or recursive computations. The observer utilized to estimate the unmeasured states is similar to a Luenberger observer with dynamic observer gains. The Lyapunov functions are quadratic in the state estimates, the observer errors, and the parameter estimation error. The stability analysis is based on our recent results on uniform solvability of coupled state-dependent Lyapunov equations. The controller design provides strong robustness properties both with respect to uncertain parameters in the system model and additive disturbances. This robustness is the key to the output feedback controller design. Global asymptotic results are obtained.     

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time‐varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.     

An output-based adaptive iterative learning controller for high relative degree uncertain linear systems

In this paper, we derive an output tracking error model based on signals filtered from plant input and output, and then present a new output-based adaptive iterative learning controller for repeatable linear systems with unknown parameters, high relative degree, initial resetting error, input disturbance and output noise. The proposed controller solves the important robustness issues without assuming the bounds of uncertainties to be sufficiently small and can be applied to high relative degree plants without using output differentiation. Control parameters are updated between successive iterations so as to compensate for unknown system parameters and uncertainties. It is shown that the internal signals inside closed-loop learning system remain bounded and the output tracking error will asymptotically converge to a profile tunable by some design parameters. Furthermore, the learning speed is easily improved if the learning gain is increased.     

Output Feedback Controller Design for systems with Amplitude and Rate Control Constraints

A method for synthesizing dynamic output feedback controllers for continuous time systems presenting actuators constrained in both amplitude and rate is proposed here. The considered controller structure is composed of a saturating integrator block connected to a linear compensator output, delivering a signal to the actuator input inside all its bounds. Considering that the plant is submitted to L ₂ bounded disturbances, linear matrix inequality conditions are proposed in order to ensure both external and internal stability of the closed loop system.     

Practical output regulation for bounded linear infinite-dimensional state space systems

We develop the mathematical foundations of practical state space output regulation for bounded infinite-dimensional linear systems. By practical output regulation we mean asymptotic tracking of references and rejection of disturbances with a given accuracy. Our main results are general upper bounds for the norms perturbations to the parameters of the exosystem, the plant and a controller which achieves exact output regulation. These bounds depend explicitly on the desired tracking accuracy ε>0. In this paper, all perturbations are assumed to be bounded, additive and linear. Our results apply for both feedforward and error feedback controllers, and for arbitrary bounded uniformly continuous reference/disturbance signals.     

线性系统极点配置控制器的鲁棒稳定性分析

本文利用所建立的线性系统鲁棒稳定性的分析结果分析了离散和连续的极点配置控制系统关于时变参数摄动在输入输出有界意义下的鲁棒稳定性。指出该控制系统对于参数摄动总具有一定的鲁棒性,并给出了保持系统输入输出有界情况下参数摄动应满足的限度。     

Dynamic Output Feedback Robust MPC Using General Polyhedral State Bounds for the Polytopic Uncertain System With Bounded Disturbance

This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints favors replacing the true state by its bound in the optimization problems. The previous utilized polyhedral bounds, constructed by virtue of the error signals which are some linear combinations of the true state, the estimated state and the output, are generalized, where a bias item is utilized. Based on this unified bounding approach, new techniques for handling the unknown true state are given for both the main and the auxiliary optimization problems. As before, the main optimization problem calculates the control law parameters conditionally, and the auxiliary optimization problem determines the time to refresh these parameters. By applying the proposed method, the augmented state of the closed‐loop system is guaranteed to converge to the neighborhood of the equilibrium point. A numerical example is given to illustrate the effectiveness of the new method.     

An algorithm for the robust exponential stabilization of a class of switched systems

In this paper, we consider continuous‐time switched systems whose subsystems are linear, or, more generally, homogeneous of degree one. For that class of systems, we present a control algorithm that under certain conditions generates switching signals that globally exponentially stabilizes the switched system, even in the case in which there are model uncertainties and/or measurement errors, provided that the bounds of that uncertainties and errors depend linearly on the norm of the state of the system and are small enough in a suitable sense. We also show that in the case in which the measurement errors and the model uncertainties are bounded, the algorithm globally exponentially stabilizes the system in a practical sense, with a final error which depends linearly on the bounds of both the model uncertainties and the measurement errors. In other words, the closed‐loop system is exponentially input‐to‐state‐stable if one considers the perturbations and output measurements bounds as inputs. For switched linear systems, under mild observability conditions, we design an observer whose state‐estimation drives the control algorithm to exponentially stabilize the system in absence of perturbations and to stabilize it in an ultimately bounded way when the perturbations and the output measurement errors are bounded. Finally, we illustrate the behavior of the algorithm by means of simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Bounded error identification of Hammerstein systems through sparse polynomial optimization

In this paper we present a procedure for the evaluation of bounds on the parameters of Hammerstein systems, from output measurements affected by bounded errors. The identification problem is formulated in terms of polynomial optimization, and relaxation techniques, based on linear matrix inequalities, are proposed to evaluate parameter bounds by means of convex optimization. The structured sparsity of the formulated identification problem is exploited to reduce the computational complexity of the convex relaxed problem. Analysis of convergence properties and computational complexity is reported.     

Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.     

Universal adaptive control of feedforward nonlinear systems with unknown input and state delays

This paper considers the problem of global asymptotic regulation via output feedback for a class of uncertain feedforward nonlinear systems with input and state delays, where the bounds of time delays are unknown. With the help of the high-gain scaling approach and the idea of universal adaptive control, we explicitly construct an adaptive output compensator with a novel positive dynamic gain which compensates simultaneously the unknown delays and the output growth rate with unknown constant. Based on such output compensator, we reduce the conservatism of the restrictive conditions imposed on nonlinearities to generalise the existing results. By the Lyapunov–Krasovskii theorem, a delay-independent controller design scheme is proposed to guarantee that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states to globally asymptotically converge to zero. Finally, two illustrative examples are given to show the usefulness of the proposed design method.     

Global regulation of almost feedforward nonlinear systems by an adaptive event-triggered controller with multi-triggering conditions

We consider a global regulation problem for almost feedforward nonlinear systems with uncertain time-varying parameters using an adaptive event-triggered controller. The systems we consider are called “almost” feedforward systems because, in addition to the feedforward nonlinearity with the unknown linear growth rate, there is a non-zero input-matching term. Notably, this input-matching term is a non-feedforward term and it cannot be directly canceled due to the presence of input uncertainty and the use of event-triggered control. To solve our considered problem, we propose an adaptive event-triggered controller with multi-triggering conditions and dynamic gain. We show that the closed-loop system is globally regulated and the times between executions are positively lower bounded. Moreover, we show that the positive lower bounds of interexecution times can be enlarged by a control parameter. For a clear illustration, a practical example is given.     

Robust performance with fixed and worst-case signals for uncertain time-varying systems

In this paper we focus our attention on the determination of upper bounds of the l^∞ norm of the output of a linear discrete-time dynamic system driven by a step input, in the presence of both persistent unknown, but, l^∞ bounded disturbances and memoryless time-varying model uncertainty. For the same type of systems we also analyze the transient behavior of the step response in terms of its overshoot. The problem is solved in a constructive way by determining appropriate invariant sets contained in a given convex region. Finally, we show how to extend these results to continuous-time systems.     

A Multi-step Output Feedback Robust MPC Approach for LPV Systems with Bounded Parameter Changes and Disturbance

This paper considers a multi-step output feedback robust model predictive control (OFRMPC) approach for the linear parameter varying (LPV) systems with bounded changes of scheduling parameters and bounded disturbance. Less conservative bounds of future estimation error sets and system parametric uncertain sets are predicted by considering bounded changes of scheduling parameters in LPV systems. In the multi-step OFRMPC approach, an optimization problem is solved to obtain a sequence of controller gains, which considers predictions of future bounds of estimation error sets and system parametric uncertain sets. The optimized sequence of controller gains corresponding to a sequence of Lyaponov matrices have less constraint conditions and also introduce more degree of freedom for the optimization. The proposed multi-step OFRMPC guarantees robust uniform ultimately bounded of the estimation error and robust stability of the observer system. A numerical example is given to demonstrate the effectiveness of the approach.     

ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs

This paper proposes a convex approach to regional stability and ℒ︁₂‐gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input‐to‐output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential‐algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ︁₂‐gain of the input‐to‐output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full‐order) output feedback controller with a guaranteed bound on the ℒ︁₂‐gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic output feedback robust MPC for LPV systems subject to input saturation and bounded disturbance

For linear parameter varying (LPV) systems with unknown scheduling parameters and bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with input saturation is investigated. By pre-specifying partial controller parameters, a main optimization problem is solved by convex optimization to reduce the on-line computational burden. The main optimization problem guarantees that the estimated state and estimation error converge within the corresponding invariant sets such that recursive feasibility and robust stability are guaranteed. The consideration of input saturation in the main optimization problem improves the control performance. Two numerical examples are given to illustrate the effectiveness of the approach.     

Output feedback robust MPC using general polyhedral and ellipsoidal true state bounds for LPV model with bounded disturbance

This paper considers the dynamic output feedback robust model predictive control (MPC) for a system with both polytopic model parametric uncertainty and bounded disturbance. For this topic, the techniques for handling the unknown true state are crucial, and the strict guarantee of the input/output/state constraints requires replacing the true state by its bounds in the optimisation problems. Previously, in the separate works, we (i) gave the general polyhedral bound; (ii) proposed the general ellipsoidal bound; (iii) applied some special polyhedral bounds to tighten the ellipsoidal bound since the latter is crucial for guaranteeing recursive feasibility. In this paper, (i)–(iii) are unified, and the up-to-date least conservative treatment of the true state bound is given, so the control performance can be greatly improved. The contribution mainly lies in overcoming the difficulties in developing technical details for the unification. A numerical example is given to illustrate the effectiveness of the new method.     

Robust regulation of a class of partially observed nonlinear continuous bioreactors

We propose a design of robust dynamic output feedback for the global partial stabilization of a class of continuous stirred bioreactors. Our approach is robust with respect to exogenous disturbances and functional uncertainties of the kinetics, considered as bounded unknown inputs. The method is based on a design of dynamic guaranteed bounds on the unmeasured variables, conditioned to past measurements and given bounds on the initial condition. This approach is suitable to systems which are not detectable for unknown inputs. The flexibility in the design of the parameters allows the consideration of saturation constraints on the control variable.