Identification of piecewise affine systems via mixed-integer programming

This paper addresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models, in which the regressor space is partitioned into polyhedra with affine submodels for each polyhedron. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimum. For the special case where the estimation data only seldom switches between the different submodels, we also suggest a way of trading off between optimality and complexity by using a change detection approach.     

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.     

Robust model predictive control using tubes

A form of feedback model predictive control (MPC) that overcomes disadvantages of conventional MPC but which has manageable computational complexity is presented. The optimal control problem, solved on-line, yields a ‘tube’ and an associated piecewise affine control law that maintains the controlled trajectories in the tube despite uncertainty; computational complexity is linear (rather than exponential) in horizon length. Asymptotic stability of the controlled system is established.     

Implicit fault-tolerant control: application to induction motors

In this paper we propose an innovative way of dealing with the design of fault-tolerant control systems. We show how the nonlinear output regulation theory can be successfully adopted in order to design a regulator able to offset the effect of all possible faults which can occur and, in doing so, also to detect and isolate the occurred fault. The regulator is designed by embedding the (possible nonlinear) internal model of the fault. This idea is applied to the design of a fault-tolerant controller for induction motors in presence of both rotor and stator mechanical faults.     

Design of robust model-based controllers via parametric programming

In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples.     

Reduced-order controllers for the H∞ control problem with unstable invariant zeros

This paper addresses the existence and design methods of reduced-order controllers for the H_∞ control problem with unstable invariant zeros in the state-space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output, where the realization is induced from a stabilizable and detectable realization of the generalized plant. This paper presents a new controller degree bound for the H_∞ control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region. When the unstable invariant zero exists, this paper shows that reduced-order controllers with orders strictly less than that of the generalized plant exist if the H_∞ control problem is solvable. Moreover, this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality-based design methods (algorithms) for constructing the reduced-order controllers. The results developed in this paper are valid both for the continuous- and discrete-time H_∞ control problems.     

Drift-free attitude estimation for accelerated rigid bodies

In this paper we study the attitude estimation problem for an accelerated rigid body using gyros and accelerometers. The application in mind is that of a walking robot and particular attention is paid to the large and abrupt changes in accelerations that can be expected in such an environment. We propose a state estimation algorithm that fuses data from rate gyros and accelerometers to give long-term drift free attitude estimates. The algorithm does not use any local parameterization of the rigid body kinematics and can thus be used for a rigid body performing any kind of rotations. The algorithm is a combination of two non-standard, but in a sense linear, Kalman filters between which a trigger based switching takes place. The kinematics representation used makes it possible to construct a linear algorithm that can be shown to give convergent estimates for this nonlinear problem. The state estimator is evaluated in simulations demonstrating how the estimates are long-term stable even in the presence of gyro drift.     

Detection filter design for LPV systems—a geometric approach

This paper investigates fault detection and isolation of linear parameter-varying (LPV) systems by using parameter-varying (C,A)-invariant subspace and parameter-varying unobservability subspaces. The so called “detection filter” approach, formulated as the fundamental problem of residual generation (FPRG) for linear time-invariant (LTI) systems, is extended for a class of LPV systems. The question of stability is addressed in the terms of Lyapunov quadratic stability by using linear matrix inequalities. The results are applied to the model of a generic small commercial aircraft.     

On the ill-conditioning of subspace identification with inputs

There is experimental evidence that the performance of standard subspace algorithms from the literature (e.g. the N4SID method) may be surprisingly poor in certain experimental conditions. This happens typically when the past signals (past inputs and outputs) and future input spaces are nearly parallel. In this paper we argue that the poor behavior may be attributed to a form of ill-conditioning of the underlying multiple regression problem, which may occur for nearly parallel regressors. An elementary error analysis of the subspace identification problem, shows that there are two main possible causes of ill-conditioning. The first has to do with near collinearity of the state and future input subspaces. The second has to do with the dynamical structure of the input signal and may roughly be attributed to “lack of excitation”. Stochastic realization theory constitutes a natural setting for analyzing subspace identification methods. In this setting, we undertake a comparative study of three widely used subspace methods (N4SID, Robust N4SID and PO-MOESP). The last two methods are proven to be essentially equivalent and the relative accuracy, regarding the estimation of the (A,C) parameters, is shown to be the same.     

A practical implementation of stochastic programming: an application to the evaluation of option contracts in supply chains

Stochastic programming is a powerful analytical method in order to solve sequential decision-making problems under uncertainty. We describe an approach to build such stochastic linear programming models. We show that algebraic modeling languages make it possible for non-specialist users to formulate complex problems and have solved them by powerful commercial solvers. We illustrate our point in the case of option contracts in supply chain management and propose a numerical analysis of performance. We propose easy-to-implement discretization procedures of the stochastic process in order to limit the size of the event tree in a multi-period environment.