Perception-Based Sampled-Data Optimization of Dynamical Systems

Motivated by perception-based control problems in autonomous systems, this paper addresses the problem of developing feedback controllers to regulate the inputs and the states of a dynamical system to optimal solutions of an optimization problem when one has no access to exact measurements of the system states. In particular, we consider the case where the states need to be estimated from high-dimensional sensory data received only at discrete time intervals. We develop a sampled-data feedback controller that is based on adaptations of a projected gradient descent method, and that includes neural networks as integral components to estimate the state of the system from perceptual information. We derive sufficient conditions to guarantee (local) input-to-state stability of the control loop. Moreover, we show that the interconnected system tracks the solution trajectory of the underlying optimization problem up to an error that depends on the approximation errors of the neural network and on the time-variability of the optimization problem; the latter originates from time-varying safety and performance objectives, input constraints, and unknown disturbances. As a representative application, we illustrate our results with numerical simulations for vision-based autonomous driving.Comment: This is an extended version of the paper accepted to IFAC World Congress 2023 for publication, containing proof

H^∞-Optimal Fractional Delay Filters

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data $H^{infty}$ optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time $H^{infty}$ optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method

Using multispectral sensor WASP-Lite to analyze harmful algal blooms

Developing methods to monitor harmful algae is a current research “hot-topic.” One type of algae, the blue-green algae or Cyanobacteria, cause blooms that can lead to a health threat to humans and animals. This research will test the use of a cost effective and temporally efficient method using multispectral remote sensing system, WASPLITE, as a monitor of algal blooms. This airborne system will be optimized to the specific application of detecting Cyanobacteria on optically complex waters. Attempts have been made in the past using existing instruments, e.g., SeaWiFS and Landsat, to provide these data, but our solution can provide more information by using optimally selected bands with very high spatial resolution. To analyze these algal blooms, standard multispectral techniques (such as band ratio, spectral curvature and principal component analysis) were used on the airborne data. These results were compared with ground truth collected concurrently with the airborne over flight. Because of the very high spatial resolution of the system, (0.7 m), compared to many commonly used satellite systems (~30m to 1km), it could be seen that the patchiness of the algae was very high. Difficulties in applying the ground truth were both technical shortcomings and were due to the nature of the algal blooms. Technical issues include the time lag between the ground sample collect and the airborne collect (the water and algae move with time), the drift of the boat during ground sampling (there was no anchor), and the error in the GPS units in both the boat and the plane. The issues due to the nature of water and algae include, sun glint in the imagery, white foam lines created by waves and wind, and most importantly, the patchiness of the algae in the water. Because the ground truth of one sample point per location was not adequate, we could not correlate the ground truth to the imagery. Qualitatively, the images did show a large variation of algae concentration in the water through the principal component analysis. Further, flow-through data from another vessel taken from the same week this research was performed, suggests that the variation that is seen in the imagery is real. Overall, this research shows the difficulties in effectively and accurately performing ground truth measurements to be used to test algorithms and methods that are applied to detecting harmful algae using remotely sensed data. The traditional ground sampling methods failed to capture the spatial variation observed in the image data. With improved techniques we are confident these methods can be used to effectively monitor algal blooms using the high spatial and temporal resolution

Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems

The deployment of advanced real-time control and optimization strategies in socially-integratedengineering systems could significantly improve our quality of life whilecreating jobs and economic opportunity. However, in cyber-physical systems such assmart grids, transportation networks, healthcare, and robotic systems, there still existseveral challenges that prevent the implementation of intelligent control strategies.These challenges include the existence of limited communication networks, dynamicand stochastic environments, multiple decision makers interacting with the system,and complex hybrid dynamics emerging from the feedback interconnection of physicalprocesses and computational devices.In this dissertation, we study the problem of designing robust control and optimizationalgorithms for cyber-physical systems using the framework of hybrid dynamicalsystems. We propose different theoretical frameworks for the design and analysis offeedback mechanisms that optimize the performance of dynamical systems without requiringan explicit characterization of their mathematical model, i.e., in a model-freeway. The closed-loop system that emerges of the interconnection of the plant with thefeedback mechanism describes, in general, a set-valued hybrid dynamical system. Thesetypes of systems combine continuous-time and discrete-time dynamics, and they usuallylack the uniqueness of solutions property. The framework of set-valued hybriddynamical systems allows us to study many complex dynamical systems that emerge indifferent engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportationsystems, autonomous robots with logic-based controllers, etc. We proposea step-by-step approach to the design of different types of discrete-time, continuous-time,hybrid, and stochastic controllers for different types of applications, extendingand generalizing different results in the literature in the area of extremum seeking control,sampled-data extremization, robust synchronization, and stochastic learning innetworked systems. Our theoretical results are illustrated via different simulations andnumerical examples

Weighted \Cal H_\infty mixed-sensitivity minimization for stable distributed parameter plants under sampled data control

summary:This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted ${\cal H}^\infty$-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a “natural” finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite- dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control