Robust observability for a class of time-varying discrete-time uncertain systems

This paper introduces a concept of robust observability for a class of uncertain discrete-time systems. This notion is an extension of the standard notion of observability for discrete-time, linear time-varying systems. The uncertainty and noise are modelled deterministically via a sum quadratic constraint. A necessary and sufficient condition for robust observability is presented in terms of existence of a suitable solution to a Riccati difference equation. The set of possible initial states given noisy measurements over a finite number of sampling periods is shown to be an ellipsoid.     

Location estimation and trajectory prediction for cellular networks with mobile base stations

This paper provides mobility estimation and prediction for a variant of the GSM network that resembles an ad hoc wireless mobile network in which base stations and users are both mobile. We propose using a Robust Extended Kalman Filter (REKF) to derive an estimate of the mobile user's next mobile base station from the user's location, heading, and altitude, to improve connection reliability and bandwidth efficiency of the underlying system. Our analysis demonstrates that our algorithm can successfully track the mobile users with less system complexity, as it requires measurements from only one or two closest mobile base stations. Further, the technique is robust against system uncertainties caused by the inherent deterministic nature of the mobility model. Through simulation, we show the accuracy of our prediction algorithm and the simplicity of its implementation.     

Nonlinear sliding mode control of an unmanned agricultural tractor in the presence of sliding and control saturation

The paper considers the problem of automatic path tracking by autonomous farming vehicles subject to wheel slips, which are characteristic for agricultural applications. Two guidance laws are proposed to solve this problem, and both explicitly take into account the constraints on the steering angle and ensure tracking an arbitrarily curved path. The first law is implemented by the pure sliding-mode controller, whereas the second one combines the sliding mode approach with a smooth nonlinear control law and requests control chattering at the reduced amplitude as compared with the first law. Mathematically rigorous proofs of global convergence and robust stability of the proposed guidance laws are presented. In doing so, the slipping effects are treated as bounded uncertainties. Simulation results and real world experiments confirm the applicability and performance of the proposed guidance approach.     

Shannon zero error capacity in the problems of state estimation and stabilization via noisy communication channels

The paper addresses state estimation and stabilization problems involving communication errors and capacity constraints. Discrete-time partially observed unstable linear systems perturbed by stochastic exogenous disturbances are studied. Unlike the classic theory, the sensor signals are transmitted to the estimator or controller over a noisy digital communication link modelled as a stochastic stationary discrete memoryless channel. It is shown that the capability of the noisy channel to ensure almost sure stabilizability/observability of the plant is identical to exactly its capability to transmit information with zero probability of error. Specifically, it is demonstrated that the standard numerical characteristic of the latter capability, i.e., the Shannon zero error capacity of the channel, constitutes the border separating the cases where the plant is and respectively, is not stabilizable/observable with probability 1.     

Synthesis of minimax optimal controllers for uncertain time-delay systems with structured uncertainty

This paper is concerned with the design of robust state feedback controllers for a class of uncertain time-delay systems. The uncertainty is assumed to satisfy a certain integral quadratic constraint. The controller proposed is a minimax optimal controller in the sense that it minimizes the maximum value of a corresponding linear quadratic cost function over all admissible uncertainties. The controller leads to an absolutely stable closed loop uncertain system and is constructed by solving a finite dimensional parameter-dependent algebraic Riccati equation.     

Novel frameworks for the design of fault‐tolerant control using optimal sliding‐mode control

This paper describes 2 schemes for a fault‐tolerant control using a novel optimal sliding‐mode control, which can also be employed as actuator redundancy management for overactuated uncertain linear systems. By using the effectiveness level of the actuators in the performance indexes, 2 schemes for redistributing the control effort among the remaining (redundant or nonfaulty) set of actuators are constructed based on an ‐based optimal sliding‐mode control. In contrast to the current sliding‐mode fault‐tolerant control design methods, in these new schemes, the level of control effort required to maintain sliding is penalised. The proposed optimal sliding‐mode fault‐tolerant control design schemes are implemented in 2 stages. In the first stage, a state feedback gain is derived using an LMI‐based scheme that can assign a number of the closed‐loop eigenvalues to a known value whilst satisfying performance specifications. The sliding function matrix related to the particular state feedback derived in the first stage is obtained in the second stage. The difference between the 2 schemes proposed for the sliding‐mode fault‐tolerant control is that the second one includes a separate control allocation module, which makes it easier to apply actuator constraints to the problem. Moreover, it will be shown that, with the second scheme, we can deal with actuator faults or even failures without controller reconfiguration. We further discuss the advantages and disadvantages of the 2 schemes in more details. The effectiveness of the proposed schemes are illustrated with numerical examples.