Author's reply: “A comment on optimal control of SISO continuous-time systems”

In the above-mentioned comment, the author points out a technical problem with the paper (Wang, Z. Q., & Sznaier, M. (1997). Automatica, 33(1), 85–90). As we show here, this technical problem can be easily solved. Moreover, it affects neither the main formulation nor the results, which remain valid.     

Segmentation for robust tracking in the presence of severe occlusion

Tracking an object in a sequence of images can fail due to partial occlusion or clutter. Robustness to occlusion can be increased by tracking the object as a set of "parts" such that not all of these are occluded at the same time. However, successful implementation of this idea hinges upon finding a suitable set of parts. In this paper we propose a novel segmentation, specifically designed to improve robustness against occlusion in the context of tracking. The main result shows that tracking the parts resulting from this segmentation outperforms both tracking parts obtained through traditional segmentations, and tracking the entire target. Additional results include a statistical analysis of the correlation between features of a part and tracking error, and identifying a cost function that exhibits a high degree of correlation with the tracking error.     

Robust controller design for a non-colocated spring-mass system via mixed 𝓁/∞ optimization

A successful controller design paradigm must take into account both model uncertainty and performance specifications. Model uncertainty can be addressed using the ??^∞ robust control framework. However, this framework cannot accommodate the realistic case where in addition to robustness considerations, the system is subject to time-domain specifications. We recently proposed design procedures to explicitly incorporate time-domain specifications into the ??^∞ framework. In this paper we apply these design procedures to the simple mass-spring system used as a benchmark in the 1990–1992 ACC, with the goal of minimizing the peak control effort while satisfying disturbance rejection, settling time, tracking and robustness specifications. The results show that there exist a severe trade-off between peak control action and robustness to unstructured model uncertainty.     

An LMI approach to control-oriented identification and model (In) validation of LPV systems

This note proposes a control-oriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on time-varying parameters as well as the possible existence of a nonparametric component. The main results of the note show that the problems of obtaining and validating a model for these systems can be recast as linear matrix inequality feasibility problems. Moreover, as the information is completed, the algorithm is shown to converge in the l/sub 2/-induced topology to the actual plant. Additional results include deterministic bounds on the identification error. These results are illustrated with a practical example arising in the context of active vision.     

An improved Voronoi-diagram-based neural net for patternclassification

We propose a novel two-layer neural network to answer a point query in R(n) which is partitioned into polyhedral regions; such a task solves among others nearest neighbor clustering. As in previous approaches to the problem, our design is based on the use of Voronoi diagrams. However, our approach results in substantial reduction of the number of neurons, completely eliminating the second layer, at the price of requiring only two additional clock steps. In addition, the design process is also simplified while retaining the main advantage of the approach, namely its ability to furnish precise values for the number of neurons and the connection weights necessitating neither trial and error type iterations nor ad hoc parameters.     

An exact solution to continuous-time mixed H/sub 2//H/sub /spl infin// control problems

Multiobjective control problems have been the object of much attention in the past few years, since they allow for handling multiple, perhaps conflicting, performance specifications and model uncertainty. One of the earliest multiobjective problems is the mixed H/sub 2//H/sub /spl infin// control problem, which can be motivated as a nominal LQG optimal control problem subject to robust stability constraints. This problem has proven to be surprisingly difficult to solve, and at this time no closed-form solutions are available. Moreover, it has been shown that except in some trivial cases, the optimal controller is infinite-dimensional. In this paper, we propose a solution to general continuous-time mixed H/sub 2//H/sub /spl infin// problems, based upon constructing a family of approximating problems, obtained by solving an equivalent discrete-time problem. Each of these approximations can be solved efficiently, and the resulting controllers converge strongly in the H/sub 2/ topology to the optimal solution.     

Mixed l1/H∞ control of MIMO systems viaconvex optimization

We present a methodology for designing mixed l₁/H_∞ controllers for MIMO systems. These controllers allow for minimizing the worst case peak output due to persistent disturbances, while at the same time satisfying an H_∞-norm constraint upon a given closed loop transfer function. Therefore, they are of particular interest for applications dealing with multiple performance specifications given in terms of the worst case peak values, both in the time and frequency domains. The main results of the paper show that: 1) contrary to the H₂/H_∞ case, the l₁/H_∞ problem admits a solution in l₁; and 2) rational suboptimal controllers can be obtained by solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and a four-block H_∞ problem. Moreover, this sequence of controllers converges in the l₁ topology to an optimum     

Rational ℒ1 suboptimal compensators forcontinuous-time systems

The persistent disturbance rejection problem (ℒ¹ optimal control) for continuous time-systems leads to nonrational compensators, even for single input/single output systems. As noted in Dahleh and Pearson (1987), the difficulty of physically implementing these controllers suggests that the most significant application of the continuous time ℒ¹ theory is to furnish achievable performance bounds for rational controllers. In this paper the authors use the theory of positively invariant sets to provide a design procedure, based upon the use of the discrete Euler approximating system, for suboptimal rational ℒ¹ controllers with a guaranteed cost. The main results of the paper show that (i) the ℒ ¹ norm of a continuous-time system is bounded above by the l ¹ norm of an auxiliary discrete-time system obtained by using the transformation z=1+rs and (ii) the proposed rational compensators yield ℒ¹ cost arbitrarily close to the optimum, even in cases where the design procedure proposed in the above mentioned paper fails due to the existence of plant zeros on the stability boundary     

H/sub 2/ control with time-domain constraints: theory and an application

In this paper, we study the problem of minimizing the H/sub 2/ norm of a given transfer function subject to time-domain constraints on the time response of a different transfer function to a given test signal. The main result of this paper shows that this problem admits a minimizing solution in R~H~/sub 2/. Moreover, rational solutions with performance arbitrarily close to optimal can be found by constructing families of approximating problems. Each one of these problems entails solving a finite-dimensional quadratic programming problem whose dimension can be determined before hand. These results are illustrated and experimentally validated by designing a controller for an active vision application.     

A model (in)validation approach to gait classification

This paper addresses the problem of human gait classification from a robust model (in)validation perspective. The main idea is to associate to each class of gaits a nominal model, subject to bounded uncertainty and measurement noise. In this context, the problem of recognizing an activity from a sequence of frames can be formulated as the problem of determining whether this sequence could have been generated by a given (model, uncertainty, and noise) triple. By exploiting interpolation theory, this problem can be recast into a nonconvex optimization. In order to efficiently solve it, we propose two convex relaxations, one deterministic and one stochastic. As we illustrate experimentally, these relaxations achieve over 83 percent and 86 percent success rates, respectively, even in the face of noisy data.