Time-Optimal Path Tracking via Reachability Analysis

Given a geometric path, the Time-Optimal Path Tracking problem consists in finding the control strategy to traverse the path time-optimally while regulating tracking errors. A simple yet effective approach to this problem is to decompose the controller into two components: (i)~a path controller, which modulates the parameterization of the desired path in an online manner, yielding a reference trajectory; and (ii)~a tracking controller, which takes the reference trajectory and outputs joint torques for tracking. However, there is one major difficulty: the path controller might not find any feasible reference trajectory that can be tracked by the tracking controller because of torque bounds. In turn, this results in degraded tracking performances. Here, we propose a new path controller that is guaranteed to find feasible reference trajectories by accounting for possible future perturbations. The main technical tool underlying the proposed controller is Reachability Analysis, a new method for analyzing path parameterization problems. Simulations show that the proposed controller outperforms existing methods.Comment: 6 pages, 3 figures, ICRA 201

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

Robust Control Barrier Functions with Uncertainty Estimation

This paper proposes a safety controller for control-affine nonlinear systems with unmodelled dynamics and disturbances to improve closed-loop robustness. Uncertainty estimation-based control barrier functions (CBFs) are utilized to ensure robust safety in the presence of model uncertainties, which may depend on control input and states. We present a new uncertainty/disturbance estimator with theoretical upper bounds on estimation error and estimated outputs, which are used to ensure robust safety by formulating a convex optimization problem using a high-order CBF. The possibly unsafe nominal feedback controller is augmented with the proposed estimator in two frameworks (1) an uncertainty compensator and (2) a robustifying reformulation of CBF constraint with respect to the estimator outputs. The former scheme ensures safety with performance improvement by adaptively rejecting the matched uncertainty. The second method uses uncertainty estimation to robustify higher-order CBFs for safety-critical control. The proposed methods are demonstrated in simulations of an uncertain adaptive cruise control problem and a multirotor obstacle avoidance situation

Optimal ripple-free deadbeat controllers

A ripple-free deadbeat controller for a system exists if and only if there are no transmission zeros coinciding with the poles of the reference signal. Approaches to this problem often use the Diophantine equation solution. However, solutions provided by the Diophantine equation often exhibit extremely bad transient responses. This approach gives a new affine parametrization of solutions of the Diophantine equation. Based on this parametrization, LMI conditions are used to provide optimal or constrained controllers for design quantities such as overshoot, undershoot, control amplitude, 'slew rate' as well as for norm bounds such as l1, l2 and l infinity

New Pinning Synchronization of Complex Networks with Time-Varying Coupling Strength and Nondelayed and Delayed Coupling

The pinning synchronization problem for a class of complex networks is studied by a stochastic viewpoint, in which both time-varying coupling strength and nondelayed and delayed coupling are included. Different from the traditionally similar methods, its interval is separated into two subintervals and described by a Bernoulli variable. Both bounds and switching probability of such subintervals are contained. Particularly, the nondelayed and delayed couplings occur alternately in which another independent Bernoulli variable is introduced. Then, a new kind of pinning controller without time-varying coupling strength signal is developed, in which only its bounds and probabilities are contained. When such probabilities are unavailable, two different kinds of adaption laws are established to make the complex network globally synchronous. Finally, the validity of the presented methods is proved through a numerical example

Controlling a Population

We introduce a new setting where a population of agents, each modelled by a finite-state system, are controlled uniformly: the controller applies the same action to every agent. The framework is largely inspired by the control of a biological system, namely a population of yeasts, where the controller may only change the environment common to all cells. We study a synchronisation problem for such populations: no matter how individual agents react to the actions of the controller, the controller aims at driving all agents synchronously to a target state. The agents are naturally represented by a non-deterministic finite state automaton (NFA), the same for every agent, and the whole system is encoded as a 2-player game. The first player chooses actions, and the second player resolves non-determinism for each agent. The game with m agents is called the m-population game. This gives rise to a parameterized control problem (where control refers to 2 player games), namely the population control problem: can playerone control the m-population game for all m in N whatever playertwo does? In this paper, we prove that the population control problem is decidable, and it is a EXPTIME-complete problem. As far as we know, this is one of the first results on parameterized control. Our algorithm, not based on cut-off techniques, produces winning strategies which are symbolic, that i they do not need to count precisely how the population is spread between states. We also show that if the is no winning strategy, then there is a population size cutoff such that playerone wins the m-population game if and only if m< cutoff. Surprisingly, cutoff can be doubly exponential in the number of states of the NFA, with tight upper and lower bounds