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There have been a number of successes in the past few years in use of formal methods for verification of real-time systems, and also in source-to-source transformation of these systems for improved analysis, performance, and schedulability. What has been lacking are formal proofs that these transformations preserve, or establish program properties. We have previously developed a set of compiler transformation rules for safe and profitable speculative execution in real-time systems. In this paper, we present formal proofs that our transformations preserve both the semantic and the timeliness properties of programs. Our approach uses temporal logic, enhanced with a denotational-semantics-like representation of program stores. While the paper focuses on the speculative execution transformations, the approach is applicable to other real-time compiler-based transformations and code optimization.

The paper surveys applications of optimal control techniques to the design of active suspensions, starting from simple quarter-car, 1D models, which are followed by their half-car, 2D, and full-car, 3D, counterparts. While the main emphasis is on Linear-Quadratic (LQ) optimal control and active suspensions, the paper also addresses a number of related subjects including semi-active suspensions; robust, adaptive and nonlinear control aspects and some of the important practical considerations. © 1997 Elsevier Science Ltd.

This paper deals with the exponential stabilizability of the class of stochastic systems with jumps. For the case of linear uncertain stochastic system, we have designed an optimal control law that guarantees the exponential stability robustness of systems with Markovian jumps. For the nonlinear case with matching conditions, we have established a similar result.

We present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed-loop stability. The scheme can be applied to both stable and unstable systems with input constraints. The objective functional to be minimized consists of an integral square error (ISE) part over a finite time horizon plus a quadratic terminal cost. The terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate Lyapunov equation. Furthermore, the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region. If the Jacobian linearization of the nonlinear system to be controlled is stabilizable, we prove that feasibility of the open-loop optimal control problem at time t=0 implies asymptotic stability of the closed-loop system. The size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense.

This work presents the extension of the results published recently. The control task is set and solved in its general form, with the number of contact force components smaller than the number of degrees of freedom of a robotic mechanism. The control methodology presented in the paper offers the possibility for synthesizing control laws, which ensure local asymptotic stability of desired robot behaviour. Simultaneous stabilization of both desired robot motion and the desired interaction force with an in advance specified transient response is achieved for cases in which the environment dynamics is described by second-order nonlinear differential equations.

This paper discusses a direct method for numerical computation of the local quadratic approximations of ( n − 1)-dimensional stable manifolds for the unstable equilibria on the stability boundary in large systems. The algorithm proposed here does not require time-consuming normal form or symbolic computations. The numerical procedure is illustrated on transient stability problems in simple power system models. © 1997 Elsevier Science Ltd.

In this paper, a robust adaptive control problem for a class of uncertain linear systems on a finite-time interval is formulated as a minimax game problem. For this class of systems, with uncertain control coefficients augmenting the state space, the system under consideration has a bilinear structure. Although the minimax solution allows for a finite-dimensional estimator, the resulting compensator structure remains much more complex than the linear-quadratic problem. For this class of partially observed systems, the minimax problem is reduced to an equivalent full information control problem where the state-space dynamics are composed of an estimator equation and its associated Riccati equation. The equivalence between the minimax adaptive controller and a saddle-point certainty equivalence adaptive controller is shown via Hamilton-Jacobi-Bellman theory where the optimal return function is differentiable. Points of discontinuity in the partial derivatives of the optimal return function are shown to form a manifold of Darboux points, from which multiple global optimal trajectories emanate. Therefore, the Dynamic Programming approach can be extended to be valid over the entire phase space, and the uniqueness of the value of the optimal return function is guaranteed. We finally show that with additional assumptions the finite-time problem can be extended to infinite time. © 1997 Elsevier Science Ltd.

Coulomb friction remains one of the major difficulties arising in control design for mechanical systems. Control of a translational pneumatic servoactuator is a typical example of such a problem. The aim of this paper is to demonstrate that sliding-mode control can be successfully used to compensate the friction of the piston in the cylinder, which is both viscous and Coulomb. A fourth-order nonlinear state-space model of a rodless pneumatic servoactuator will be developed with both numerical simulation and experimental validation. The comparison of sliding-mode control with classic PID control will be presented. © 1997 Elsevier Science Ltd.

In this paper, the authors design, analyze and simulate a roadway controller for an automated highway system (AHS) that achieved desired traffic densities along the freeway lane. A macroscopic traffic flow model that is modified for AHS operation is used for control design and analysis. Simulation results illustrate the effectiveness of the proposed controller and the benefits that AHS can bring to traffic flow.

The H ∞ control problem with constant scaling is considered. This problem is known to reduce to a search for matrices satisfying linear matrix inequalities (LMIs) and an additional nonconvex constraint. Recently, globally convergent algorithms to solve this nonconvex feasibility problem have been proposed. A major factor that determines the computational complexity is the number of nonconvex constraints. This paper gives verifiable conditions on the plant under which the reduction of nonconvex constraints is possible. The conditions appear to be a strong requirement, but in fact, they are nautrally satisfied in certain problems. © 1997 Elsevier Science Ltd.

This paper proposes a new identification method for the discrete-time impulse response model of a linear system from sampled input-output data. Our attention is especially focused on identification of the impulse response, which includes high-frequency components locally. The continuous-time impulse response of the system is approximated by a multiresolution neural network composed of the scaling and wavelet functions. Hence the system under study can be viewed as the weighted sum of a group of subsystems in which the scaling functions and wavelet functions are interpreted as their impulse responses respectively. Then the genetic algorithm and the AIC are introduced to select significant subsystems at each resolution level such that some redundant subsystems that are sensitive to the noise effects are discarded. It is shown through a simulation that the proposed method yields accurate estimate of the impulse response, even in the ill-conditioned cases. © 1997 Elsevier Science Ltd.

This paper proposes a method to estimate the non-parametric frequency-response functions of the linear parts of a Wiener-Hammerstein model using specially designed periodic excitation signals. Weak assumptions are made concerning the static nonlinearity. The estimator is developed within a stochastic errors-in-variables framework. The applicability of the method is illustrated using simulations. © 1997 Elsevier Science Ltd.

This paper is concerned with robust stabilization for linear and bilinear systems with nonlinear uncertainty. By using quadratic Lyapunov functions, our controls guarantee the uniform exponential stability of uncertain systems. Moreover, the controls have a simple structure and are easily handled. Some problems of H∞ control for these systems are also considered. © 1997 Elsevier Science Ltd.

This paper investigates the use of nonregular (not necessarily regular) static/dynamic state feedbacks to achieve feedback linearization of affine nonlinear systems. First, we provide an example that is nonregular static feedback linearizable but is not regular dynamic feedback linearizable. Then we present some preliminary necessary conditions as well as sufficient conditions for nonregular feedback linearization. The sufficient conditions are checkable, and if they are verified, a linearizing feedback could be calculated following a recursive procedure, provided that the integrations of a set of completely integrable systems are available. © 1997 Elsevier Science Ltd.

The problem of ‘structure from motion’ concerns the reconstruction of the three-dimensional structure of a scene from its projection onto a moving two-dimensional surface. Such a problem is solved effectively by the human visual system, judging from the ease with which we perform delicate control tasks involving vision as a sensor such as reaching for objects in the environment or driving a car. In this paper we study ‘structure from motion’ from the point of view of dynamical systems: we first formalize the problem of 3-D structure and motion reconstruction as the estimation of the state of certain nonlinear dynamical models. Then we study the feasibility of ‘structure from motion’ by analyzing the observability of such models. The models that define the visual motion estimation problem for feature points in the Euclidean 3-D space are not locally observable; however, the non-observable manifold can be easily isolated by imposing metric constraints on the state space. One of the peculiarities of vision as a sensor is its richness , which can be a disadvantage when we are interested only in few of the unknown parameters. For instance, if we want to control the direction of heading of our car by measuring brightness values on our retina, we have to overcome the effects that the shape of the environment, its reflectance properties, illumination and other quantities have on our measurements. Invariance to undesired parameters can be achieved by appropriate modeling or by choice of representation of the parameter space. We propose and analyze models for 3-D structure that are independent of 3-D motion and vice versa. Estimating unknown parameters from such models amounts to the identification of nonlinear and implicit systems with parameters on differentiable manifolds, such as a sphere or the so-called essential manifold . © 1997 Elsevier Science Ltd.

This paper presents a new method for deriving robust stability conditions for single-input/single-output (SISO) model predictive control algorithms, based on an application of Jury's dominant coefficient lemma. Model uncertainty is parameterized by a range of possible plant impulse responses. The method is illustrated by deriving robust stability conditions for the extended-horizon predictive control algorithms EHPC1 and EHPC2, as well as for a prototypical model predictive controller presented originally by Garcia and Morari. © 1997 Elsevier Science Ltd.

In this paper we introduce a robust control design method for solving linear optimal control problems with fixed terminal time and fixed terminal constraints. We propose the use of a sliding mode, and introduce a new manifold design approach, since the existing approaches do not adequately address the above class of problems. The class of time-varying sliding-mode manifolds introduced is shown to result in control designs optimal with respect to quadratic cost defined over a finite time interval. © 1997 Elsevier Science Ltd.

We consider an N -machine flowshop with unreliable machines and bounds on work-in-process. Machine capacities and demand processes are finite-state Markov chains. The problem is to choose the rates of production on the machines over time to minimize the expected discounted costs of production and inventory/backlog. We show that the value function of the problem is locally Lipschitz and is a solution to a dynamic programming equation with a certain boundary condition. We provide a verification theorem, and derive the optimal feedback control policy in terms of the directional derivatives of the value function. © 1997 Elsevier Science Ltd.

A new method for the identification of the nonlinear Hammerstein model, consisting of a static nonlinear part in cascade with a linear dynamic part, is introduced. The static nonlinear part is modeled by a multilayer feedforward neural network (MFNN), and the linear part is modeled by an autoregressive moving average (ARMA) model. A recursive algorithm is developed for estimating the weights of the MFNN and the parameters of ARMA model. Simulation examples are included to illustrate the performance of the proposed method. © 1997 Elsevier Science Ltd.

We consider the problem of identifying multivariable finite dimensional linear time-invariant systems from noisy input/output measurements. Apart from the fact that both the measured input and output are corrupted by additive white noise, the output may also be contaminated by a term which is caused by a white input process noise; furthermore, all these noise processes are allowed to be correlated with each other. We shall develop a solution to this problem in the framework of subspace identification and we shall show that our algorithms give consistent estimates when the system is operating in open- or closed-loop. Two realistic simulation studies are presented to demonstrate the practical applicability of the proposed algorithms. © 1997 Elsevier Science Ltd.

Multipliers are used in stability theory to reduce conservatism and exploit structural information about system components. For an important class of stability problems, which gives a resulting infinite-dimensional multiplier optimization, a corresponding dual problem is stated. The dual gives valuable information about the original problem, in particular error bounds for its finite-dimensional approximations. © 1997 Elsevier Science Ltd.

A tracking control methodology via time-varying state feedback based on the backstepping technique is proposed for both a kinematic and simplified dynamic model of a two-degrees-of-freedom mobile robot. We first address the local tracking problem where initial tracking errors are sufficiently small. Then, under additional conditions on the desired velocities, we treat the global tracking problem where initial tracking errors are arbitrary. Simulation results are provided to validate and analyse our theoretical results.

Several robustness problems such as stability and performance robustness analysis of feedback systems and robust design of control systems in the presence of mixed nonlinear parametric and nonparametric perturbations can be solved by means of algorithms based on interval-arithmetic computation. Some of the main algorithms available in the literature are presented, and their efficiency is tested on some examples of robustness analysis and design of control systems. © 1997 Elsevier Science Ltd.

The problem of robust disturbance rejection with simultaneous robust input-output decoupling of linear systems with nonlinear uncertain structure is solved. The controller is static and independent of the uncertainties. The necessary and sufficient conditions for the problem to have a solution via state feedback are established. The general analytical expressions of the feedback matrices and the decoupled closed-loop system are derived. The closed-loop system structural properties of pole assignment and stabilizability are studied. © 1997 Elsevier Science Ltd.

We present a new systematic procedure to find low-order linear fractional representations of systems with polynomial parametric uncertainty. The idea is to exploit the structure of the uncertainty to decompose a multidimensional polynomial matrix into sums and products of simple factors for which minimal linear fractional representations can be obtained. This approach is implemented in the structured tree decomposition algorithm, which generates a tree whose leaves are simple factors. An example is presented to illustrate the advantages of this approach. © 1997 Elsevier Science Ltd.