Co-Design of Autonomous Systems: From Hardware Selection to Control Synthesis

Designing cyber-physical systems is a complex task which requires insights at multiple abstraction levels. The choices of single components are deeply interconnected and need to be jointly studied. In this work, we consider the problem of co-designing the control algorithm as well as the platform around it. In particular, we leverage a monotone theory of co-design to formalize variations of the LQG control problem as monotone feasibility relations. We then show how this enables the embedding of control co-design problems in the higher level co-design problem of a robotic platform. We illustrate the properties of our formalization by analyzing the co-design of an autonomous drone performing search-and-rescue tasks and show how, given a set of desired robot behaviors, we can compute Pareto efficient design solutions.Comment: 8 pages, 6 figures, to appear in the proceedings of the 20th European Control Conference (ECC21

Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach

We introduce a real-time, constrained, nonlinear Model Predictive Control for the motion planning of legged robots. The proposed approach uses a constrained optimal control algorithm known as SLQ. We improve the efficiency of this algorithm by introducing a multi-processing scheme for estimating value function in its backward pass. This pass has been often calculated as a single process. This parallel SLQ algorithm can optimize longer time horizons without proportional increase in its computation time. Thus, our MPC algorithm can generate optimized trajectories for the next few phases of the motion within only a few milliseconds. This outperforms the state of the art by at least one order of magnitude. The performance of the approach is validated on a quadruped robot for generating dynamic gaits such as trotting.Comment: 8 page

A final report of research on stochastic and adaptive systems under grant AFOSR 77-3281B for the period February 1, 1978 to January 31, 1979

Final report"March 1979."Bibliography: p. 17-19.Grant AFOSR-77-3281Bby Michael Athans and Sanjoy K. Mitter

Team decision theory of switched static and dynamic systems

This dissertation considers the decentralized control of switched linear systems with parameter dependent cost and system matrices. This problem class is investigated under a number of different formulations of player information structure, performance criteria and switching architecture. Such decentralized switched systems can be encountered in various applications like network control, control in a changing environment, economic theory, power systems, decision making in organizations, resource allocation. The thesis is roughly divided into three parts. The first part of the thesis focuses on the static quadratic team problem, where players observe partial observations of an underlying random state and generate actions with the objective of minimizing the expected value of a common quadratic cost function in the player actions. One of the motivations behind studying this problem is to solve a static stochastic-parameter problem useful in solving dynamic switched control problems encountered later. The problem however is studied in full generality and an operator theoretic framework is presented to analyze the same. We prove that a scheme where strategies are updated by sequentially applying the best responses of players, converges to the team optimal strategy. Such an update scheme provides a mechanism to numerically compute arbitrarily close approximations of the team optimal strategy. It also acts as a tool for validating structure of the team optimal strategy which can be beneficial in some cases for analytical computation of these strategies. The second part of the thesis considers dynamic switched optimal control problems with quadratic cost and players having local parameter knowledge. One of these problems is studied under full state feedback and i.i.d. parameter; the remaining two problems are output feedback, distinguished by the type of information structure: partially nested and one-step delayed sharing. For the former output feedback problem, parameters and measurements follow a partially nested structure with the parameters possibly being correlated across all stages. For the latter case, parameters are assumed to be Markov processes, with their values along with measurements available instantaneously to local controllers, but with a one time step delay to others. The solution to all these problems rely on the optimal solution to a static (one-stage) stochastic-parameter problem with local parameter dependent Gaussian measurements, and for this purpose the static quadratic team problem, examined in first part is used. The strategies obtained in all these dynamic problems are affine in the measurements with the parameter dependent coefficients obtained by solving a set of linear equations. These equations are immediately solvable when the total number of parameter values is finite. However, for the case of infinite parameter values, the update scheme examined in the first section also provides a mechanism to determine an approximation to the team optimal strategy. In the final part of the thesis, we consider a setup with switched linear nested plant whose system matrices switch between a finite number of values, with transitions in time governed by a finite state automaton. A linear nested controller is sought with corresponding system matrices dependent on a finite path history of the plant’s system matrices in order to stabilize the plant and achieve a desired level of l2-induced norm performance. The nested structures of both plant and controller are characterized by block lower-triangular system matrices with compatible dimensions. For this setup, exact conditions are provided for the existence of a finite path dependent synthesis. These include conditions for the completion of scaling matrices obtained through an extended matrix completion lemma. When individual controller dimensions are chosen at least as large as the plant, these conditions reduce to a set of linear matrix inequalities. The completion lemma also provides an algorithm to complete the closed loop scaling matrices leading to inequalities for controller synthesis

On Control and Estimation of Large and Uncertain Systems

This thesis contains an introduction and six papers about the control and estimation of large and uncertain systems. The first paper poses and solves a deterministic version of the multiple-model estimation problem for finite sets of linear systems. The estimate is an interpolation of Kalman filter estimates. It achieves a provided energy gain bound from disturbances to the point-wise estimation error, given that the gain bound is feasible. The second paper shows how to compute upper and lower bounds for the smallest feasible gain bound. The bounds are computed via Riccati recursions. The third paper proves that it is sufficient to consider observer-based feedback in output-feedback control of linear systems with uncertain parameters, where the uncertain parameters belong to a finite set. The paper also contains an example of a discrete-time integrator with unknown gain. The fourth paper argues that the current methods for analyzing the robustness of large systems with structured uncertainty do not distinguish between sparse and dense perturbations and proposes a new robustness measure that captures sparsity. The paper also thoroughly analyzes this new measure. In particular, it proposes an upper bound that is amenable to distributed computation and valuable for control design. The fifth paper solves the problem of localized state-feedback L2 control with communication delay for large discrete-time systems. The synthesis procedure can be performed for each node in parallel. The paper combines the localized state-feedback controller with a localized Kalman filter to synthesize a localized output feedback controller that stabilizes the closed-loop subject to communication constraints. The sixth paper concerns optimal linear-quadratic team-decision problems where the team does not have access to the model. Instead, the players must learn optimal policies by interacting with the environment. The paper contains algorithms and regret bounds for the first- and zeroth-order information feedback

On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.Comment: 19 pages, 3 figure