A suboptimal active disturbance rejection controller (S-ADRC) is proposed for second-order systems with unknown time-varying nonlinear dynamics. The output-feedback controller guarantees a global convergence to the vicinity of an optimal solution by means of dynamic control gains, based on the estimated main and extended state variables obtained through a high-gain observer. Three numerical examples compare the performance of the proposed control scheme applied to linear and nonlinear systems with that of a fixed-gain conventional ADRC as well as several model-based optimal and suboptimal controllers.
This paper presents a novel adaptive control methodology for uncertain systems with time-varying unknown parameters and time-varying bounded disturbance. The adaptive controller ensures uniformly bounded transient and asymptotic tracking for system's both signals, input and output, simultaneously. The performance bounds can be systematically improved by increasing the adaptation gain. Simulations of a robotic arm with time-varying friction verify the theoretical findings.
We present a data-driven model predictive control scheme for chance-constrained Markovian switching systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show…
Adaptive cooperative tracking control with prescribed performance function (PPF) is proposed for high-order nonlinear multi-agent systems. The tracking error originally within a known large set is confined to a smaller predefined set using this approach. Using output error transformation, the constrained system is relaxed and mapped to an unconstrained one. The controller is conceived under the assumption that the agents' nonlinear dynamics are unknown and the perceived network is structured and strongly connected. Under the proposed controller, all agents track the trajectory of the leader no…
The problem of computing the reachable set for a given system is a quintessential question in nonlinear control theory. While previous work has yielded a plethora of approximate and analytical methods for determining such a set, these methods naturally require the knowledge of the controlled system dynamics throughout the state space. In contrast to such classical methods, this paper considers the question of estimating the reachable set of a control system using only the knowledge of local system dynamics at a single point and a bound on the rate of change of dynamics. Namely, motivated by th…
California Institute of Technology（加州理工学院）；University of California San Diego（加州大学圣地亚哥分校）；Carnegie Mellon University（卡内基梅隆大学）；Purdue University（普渡大学）
Learning a dynamical system requires stabilizing the unknown dynamics to avoid state blow-ups. However, current reinforcement learning (RL) methods lack stabilization guarantees, which limits their applicability for the control of safety-critical systems. We propose a model-based RL framework with formal stability guarantees, Krasovskii Constrained RL (KCRL), that adopts Krasovskii's family of Lyapunov functions as a stability constraint. The proposed method learns the system dynamics up to a confidence interval using feature representation, e.g. Random Fourier Features. It then solves a const…
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper, a modular design methodology is formulated, that consists of three design phases: (i) an initial robust observer design that enables one to learn the dynamics without allowing the state estimation error to diverge (hence, safe); (ii) a learning phase wherein the unmodeled components are estimated using Bayesian optimization and Gaussian processes; and, (iii…
We investigate the problem of data-driven, on-the-fly control of systems with unknown nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side information on the dynamics are available. Such side information may include knowledge of the regularity of the dynamics, monotonicity of the states, or decoupling in the dynamics between the states. Specifically, we develop two algorithms, $\texttt{DaTaReach}$ and $\texttt{DaTaControl}$, to over-approximate the reachable set and design control signals for the system on the fly. $\texttt{DaTaReach}$ constructs a diffe…
In this paper we design suboptimal control laws for an unknown linear system on the basis of measured data. We focus on the suboptimal linear quadratic regulator problem and the suboptimal H2 control problem. For both problems, we establish conditions under which a given data set contains sufficient information for controller design. We follow up by providing a data-driven parameterization of all suboptimal controllers. We will illustrate our results by numerical simulations, which will reveal an interesting trade-off between the number of collected data samples and the achieved controller per…
We develop data-driven algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms not only are suitable for settings with real-time requirements but also provide provable performance guarantees. To this end, they merge noisy data from only a single finite-horizon trajectory and, if available, various forms of side information. Such side information may include knowledge of the regularity of the dynamics, algebraic constraints on the states, monotonicity, or decoupling in the dynamics between the states. Specifically, we develo…
Recent work in data-driven control has revived behavioral theory to perform a variety of complex control tasks, by directly plugging libraries of past input-output trajectories into optimal control problems. Despite recent advances, a key aspect remains unclear: how and to what extent do noise-corrupted data impact control performance? In this work, we provide a quantitative answer to this question. We formulate a Behavioral version of the Input-Output Parametrization (BIOP) for the optimal predictive control of unknown systems using output-feedback dynamic control policies. The main advantage…
We study the problem of data-driven, constrained control of unknown nonlinear dynamics from a single ongoing and finite-horizon trajectory. We consider a one-step optimal control problem with a smooth, black-box objective, typically a composition of a known cost function and the unknown dynamics. We investigate an on-the-fly control paradigm, i.e., at each time step, the evolution of the dynamics and the first-order information of the cost are provided only for the executed control action. We propose an optimization-based control algorithm that iteratively minimizes a data-driven surrogate fun…
In the context of the linear programming (LP) approach to data-driven control, one assumes that the dynamical system is unknown but can be observed indirectly through data on its evolution. Both theoretical and empirical evidence suggest that a desired suboptimality gap is often only achieved with massive exploration of the state-space. In case of linear systems, we discuss how a relatively small but sufficiently rich dataset can be exploited to generate new constraints offline and without observing the corresponding transitions. Moreover, we show how to reconstruct the associated unknown stag…
This work presents a method of efficiently computing inner and outer approximations of forward reachable sets for nonlinear control systems with changed dynamics and diminished control authority, given an a priori computed reachable set for the nominal system. The method functions by shrinking or inflating a precomputed reachable set based on prior knowledge of the system's trajectory deviation growth dynamics, depending on whether an inner approximation or outer approximation is desired. These dynamics determine an upper bound on the minimal deviation between two trajectories emanating from t…
The paper addresses the problem of optimization of a guaranteed (worst case) result for a control system driven by a controlling side in presence of a dynamical disturbance. The disturbances as functions of time are subject to functional constraints belonging to a given family of constraints. The latter family is known to the controlling side that does not observe the disturbance and uses full-memory strategies to form the control actions. The study is focused on the case where disturbance varies in open-loop disturbances chosen in advance and the case where the disturbances are restricted to …
We rely on Nagumo's invariance theorem to develop a new approach for navigation in unknown environments of arbitrary dimension. The idea consists in projecting the nominal velocities (that would drive the robot to the target in the absence of obstacles) onto Bouligand's tangent cones (referred to as the safety velocity cones) when the robot is close to the boundary of the free space. The proposed projection-based controller is explicitly constructed to guarantee safety and convergence to a set of Lebesgue measure zero that contains the target. For specific free spaces such as Euclidean sphere …
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport theory, the proposed method generates a graph connecting the initial and target configurations, and then finds a path over the graph using the available environmental information. The graph and path are updated iteratively when newly encountered obstacle information becomes available. The resulting method is a deterministic procedure proven to be complete, i.e…
Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This paper is motivated by a scenario where a system suffers an adverse event mid-operation, resulting in a substantial change to the system's dynamics, rendering them largely unknown. Our objective is to conservatively approximate the system's reachable set solely from its local dynamics at a single point and the bounds on the rate of change of its dynamics. We translate this knowledge about the…
This thesis presents fuzzy-L1 adaptive controller and Model Reference Adaptive Control (MRAC) with Prescribed Performance Function (PPF) as two adaptive approaches for high nonlinear systems as two original contribution to the literature. L1 adaptive controller has a structure that allows decoupling between robustness and adaption owing to the use of a low pass filter with adjustable gain in the feedback loop. A practical new fuzzy based approach for the tuning of the feedback filter of L1 adaptive controller is proposed. The fuzzy controller is optimally tuned using Particle Swarm Optimizatio…
