ε-bounded state estimation for time-delay systems with bounded disturbances

A new problem on ε-bounded functional state estimation for time-delay systems with unknown bounded disturbances is studied in this paper. In the presence of unknown bounded disturbances, the common assumption regarding the observers matching condition is no longer required. In this regard, instead of achieving asymptotic convergence for the observer error, the error is now required to converge exponentially within a ball with a small radius ε > 0. This means that the estimate converges exponentially within an ε-bound of the true value. A general observer that utilises multiple-delayed output and input information is proposed. Sufficient conditions for the existence of the proposed observer are first given. We then employ an extended Lyapunov-Krasovskii functional which combines the delay-decomposition technique with a triple-integral term to study the ε-convergence problem of the observer error system. Moreover, the obtained results are shown to be more effective than the existing results for the cases with no disturbances and/or no time delay. Three numerical examples are given to illustrate the obtained results.

Reachable sets bounding for switched systems with time-varying delay and bounded disturbances

In this paper, we address the problem of finding outer bound of forward reachable sets and inter-bound of backward reachable sets of switched systems with an interval time-varying delay and bounded disturbances. By constructing a flexible Lyapunov–Krasovskii functional combining with some recent refined integral-based inequalities, some sufficient conditions are derived for the existence of (1) the smallest possible outer bound of forwards reachable sets; and (2) the largest possible inter-bound of backward reachable sets. These conditions are delay dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. A constructive geometric design of switching laws is also presented. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

Reachable sets bounding for generalized neural networks with interval time-varying delay and bounded disturbances

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov–Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results.

Identification of linear systems in the presence of piecewise polynomial disturbances

The paper proposes a method of performing system identification of a linear system in the presence of bounded disturbances. The disturbances may be piecewise parabolic or periodic functions. The method is demonstrated effectively on two example systems with a range of disturbances.

Linear functional observers with guaranteed ε-convergence for discrete time-delay systems with input/output disturbances

The problem of designing linear functional observers for discrete time-delay systems with unknown-but-bounded disturbances in both the plant and the output is considered for the first time in this paper. A novel approach to design a minimum-order observer is proposed to guarantee that the observer error is ϵ-convergent, which means that the estimate converges robustly within an ϵ-bound of the true state. Conditions for the existence of this observer are first derived. Then, by utilising an extended Lyapunov-Krasovskii functional and the free-weighting matrix technique, a sufficient condition for ϵ-convergence of the observer error system is given. This condition is presented in terms of linear matrix inequalities with two parameters needed to be tuned, so that it can be efficiently solved by incorporating a two-dimensional search method into convex optimisation algorithms to obtain the smallest possible value for ϵ. Three numerical examples, including the well-known single-link flexible joint robotic system, are given to illustrate the feasibility and effectiveness of our results.

Componentwise ultimate bounds for positive discrete time-delay systems perturbed by interval disturbances

This paper presents a method to derive componentwise ultimate upper bounds and componentwise ultimate lower bounds for linear positive systems with time-varying delays and bounded disturbances. The disturbance vector is assumed to vary within a known interval whose lower bound may be different from zero. We first derive a sufficient condition for the existence of componentwise ultimate bounds. This condition is given in terms of the spectral radius of the system matrices which is easy to check and allows us to compute directly both the smallest componentwise ultimate upper bound and the largest componentwise ultimate lower bound. Then, by using the comparison method, we extend the obtained result to a class of nonlinear time-delay systems which has linear positive bounds. Two numerical examples are given to illustrate the effectiveness of the obtained results.

Robust multiplexed model predictive control

This paper extends the recently developed multiplexed model predictive control (MMPC) concept to ensure satisfaction of hard constraints despite the action of persistent, unknown but bounded disturbances. MMPC uses asynchronous control moves on each input channel instead of synchronised moves on all channels. It offers reduced computation, by dividing the online optimisation into a smaller problem for each channel, and potential performance improvements, as the response to a disturbance is quicker, albeit via only one channel. Robustness to disturbances is introduced using the constraint tightening approach, tailored to suit the asynchronous updates of MMPC and the resulting time-varying optimisations. Numerical results are presented, involving a simple mechanical example and an aircraft control example, showing the potential computational and performance benefits of the new robust MMPC.

Robust variable horizon MPC with move blocking

This paper introduces a new formulation of variable horizon model predictive control (VH-MPC) that utilises move blocking for reducing computational complexity. Various results pertaining to move blocking are derived, following which, a generalised blocked VH-MPC controller is formulated for linear discrete-time systems. Robustness to bounded disturbances is ensured through the use of tightened constraints. The resulting time-varying control scheme is shown to guarantee robust recursive feasibility and finite-time completion. An example is then presented for a particular choice of blocking regime, as would be applicable to vehicle manœuvring problems. Simulations demonstrate the efficacy of the formulation. © 2012 Elsevier B.V. All rights reserved.

Robust multiplexed MPC for distributed multi-agent systems

This paper extends the authors' earlier work which adapted robust multiplexed MPC for application to distributed control of multi-agent systems with non-interacting dynamics and coupled constraint sets in the presence of persistent unknown, but bounded disturbances. Specifically, we propose exploiting the single agent update nature of the multiplexed approach, and fix the update sequence to enable input move-blocking and increased discretisation rates. This permits a higher rate of individual policy update to be achieved, whilst incurring no additional computational cost in the corresponding optimal control problems to be solved. A disturbance feedback policy is included between updates to facilitate finding feasible solutions. The new formulation inherits the property of rapid response to disturbances from multiplexing the control and numerical results show that fixing the update sequence does not incur any loss in performance. © 2011 IFAC.

Robust predictive control with feasible contingencies for fault tolerance

This paper introduces the notion of M-step robust fault tolerance for discrete-time systems where finite-time completion of a control manoeuvre is desired. It considers a scenario with two distinct objectives; a primary and secondary target are specified as sets to be reached in finite-time, whilst satisfying operating constraints on the states and inputs. The primary target is switched to the secondary target when a fault affects the system. As it is unknown when or if the fault will occur, the trajectory to the primary target is constrained to ensure reachability of the secondary target within M steps. A variable-horizon linear MPC formulation is developed to illustrate the concept. The formulation is then extended to provide robustness to bounded disturbances by use of tightened constraints. Simulations demonstrate the efficacy of the controller formulation on a double-integrator model. © 2011 IFAC.

Reachable set bounding for nonlinear perturbed time-delay systems: the smallest bound

In this letter, we propose a new approach to obtain the smallest box which bounds all reachable sets of a class of nonlinear time-delay systems with bounded disturbances. A numerical example is studied to illustrate the obtained result.

Linear functional state bounding for perturbed time-delay systems and its application

This paper considers time-delay systems with bounded disturbances. We study a new problem of finding an upper bound of an absolute value function of any given linear functional of the state vector starting from the origin of the system. Based on the Lyapunov-Krasovskii method combining with the recent Wirtinger-based integral inequality that has just been proposed by Seuret & Gouaisbaut (2013. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 49, 2860-2866), sufficient conditions for the existence of an upper bound of the function are derived. The obtained results are shown to be more effective than those adapted from the existing works on reachable set bounding. Furthermore, the obtained results are applied to refine existing ellipsoidal bounds of the reachable sets. The effectiveness of the obtained results is illustrated by two numerical examples.