18 research outputs found
Reachability-based Identification, Analysis, and Control Synthesis of Robot Systems
We introduce reachability analysis for the formal examination of robots. We
propose a novel identification method, which preserves reachset conformance of
linear systems. We additionally propose a simultaneous identification and
control synthesis scheme to obtain optimal controllers with formal guarantees.
In a case study, we examine the effectiveness of using reachability analysis to
synthesize a state-feedback controller, a velocity observer, and an output
feedback controller.Comment: This work has been submitted to the IEEE for possible publication.
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Robust model predictive control for linear sampled-data systems with irregular sampling times
This paper presents a sampled-data tube-based robust MPC scheme for linear continuous-time systems with irregular sampling times. The sampled-data control law is updated only at discrete sampling instances, but the proposed controller guarantees constraint satisfaction of the continuous-time state for all times. The proposed MPC scheme allows for two sources of uncertainty, (i) uncertain sampling times and (ii) an additional disturbance to the continuous-time system. A constraint adaptation is presented to handle this setting in a rigid tube MPC framework. Constraint satisfaction and convergence of the continuous-time state are shown for the proposed MPC scheme
Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes
While reinforcement learning produces very promising results for many
applications, its main disadvantage is the lack of safety guarantees, which
prevents its use in safety-critical systems. In this work, we address this
issue by a safety shield for nonlinear continuous systems that solve
reach-avoid tasks. Our safety shield prevents applying potentially unsafe
actions from a reinforcement learning agent by projecting the proposed action
to the closest safe action. This approach is called action projection and is
implemented via mixed-integer optimization. The safety constraints for action
projection are obtained by applying parameterized reachability analysis using
polynomial zonotopes, which enables to accurately capture the nonlinear effects
of the actions on the system. In contrast to other state-of-the-art approaches
for action projection, our safety shield can efficiently handle input
constraints and dynamic obstacles, eases incorporation of the spatial robot
dimensions into the safety constraints, guarantees robust safety despite
process noise and measurement errors, and is well suited for high-dimensional
systems, as we demonstrate on several challenging benchmark systems
Model Predictive Control for Micro Aerial Vehicles: A Survey
This paper presents a review of the design and application of model
predictive control strategies for Micro Aerial Vehicles and specifically
multirotor configurations such as quadrotors. The diverse set of works in the
domain is organized based on the control law being optimized over linear or
nonlinear dynamics, the integration of state and input constraints, possible
fault-tolerant design, if reinforcement learning methods have been utilized and
if the controller refers to free-flight or other tasks such as physical
interaction or load transportation. A selected set of comparison results are
also presented and serve to provide insight for the selection between linear
and nonlinear schemes, the tuning of the prediction horizon, the importance of
disturbance observer-based offset-free tracking and the intrinsic robustness of
such methods to parameter uncertainty. Furthermore, an overview of recent
research trends on the combined application of modern deep reinforcement
learning techniques and model predictive control for multirotor vehicles is
presented. Finally, this review concludes with explicit discussion regarding
selected open-source software packages that deliver off-the-shelf model
predictive control functionality applicable to a wide variety of Micro Aerial
Vehicle configurations
Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction
We show that, for any spatially discretized system of reaction-diffusion, the
approximate solution given by the explicit Euler time-discretization scheme
converges to the exact time-continuous solution, provided that diffusion
coefficient be sufficiently large. By "sufficiently large", we mean that the
diffusion coefficient value makes the one-sided Lipschitz constant of the
reaction-diffusion system negative. We apply this result to solve a finite
horizon control problem for a 1D reaction-diffusion example. We also explain
how to perform model reduction in order to improve the efficiency of the
method
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Self-triggered MPC with performance guarantee using relaxed dynamic programming
This paper presents a self-triggered MPC controller design strategy for linear systems with state and input constraints. Based on the so-called relaxed dynamic programming inequality, the synthesis procedure determines both the updated MPC control action and the next triggering time. The resulting self-triggered MPC control law preserves stability and constraint satisfaction
and also satis es a certain speci fied performance requirement without requiring stabilizing terminal constraints. A robust self-triggered MPC scheme, based on the tube-MPC idea, is also presented for linear systems with persistent bounded additive disturbances. Simulation examples illustrate the e ffectiveness of our proposed self-triggered MPC scheme
Linear tracking MPC for nonlinear systems Part I: The model-based case
We develop a tracking model predictive control (MPC) scheme for nonlinear
systems using the linearized dynamics at the current state as a prediction
model. Under reasonable assumptions on the linearized dynamics, we prove that
the proposed MPC scheme exponentially stabilizes the optimal reachable
equilibrium w.r.t. a desired target setpoint. Our theoretical results rely on
the fact that, close to the steady-state manifold, the prediction error of the
linearization is small and hence, we can slide along the steady-state manifold
towards the optimal reachable equilibrium. The closed-loop stability properties
mainly depend on a cost matrix which allows us to trade off performance,
robustness, and the size of the region of attraction. In an application to a
nonlinear continuous stirred tank reactor, we show that the scheme, which only
requires solving a convex quadratic program online, has comparable performance
to a nonlinear MPC scheme while being computationally significantly more
efficient. Further, our results provide the basis for controlling nonlinear
systems based on data-dependent linear prediction models, which we explore in
our companion paper
A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis
In this work, we analyze an efficient sampling-based algorithm for
general-purpose reachability analysis, which remains a notoriously challenging
problem with applications ranging from neural network verification to safety
analysis of dynamical systems. By sampling inputs, evaluating their images in
the true reachable set, and taking their -padded convex hull as a set
estimator, this algorithm applies to general problem settings and is simple to
implement. Our main contribution is the derivation of asymptotic and
finite-sample accuracy guarantees using random set theory. This analysis
informs algorithmic design to obtain an -close reachable set
approximation with high probability, provides insights into which reachability
problems are most challenging, and motivates safety-critical applications of
the technique. On a neural network verification task, we show that this
approach is more accurate and significantly faster than prior work. Informed by
our analysis, we also design a robust model predictive controller that we
demonstrate in hardware experiments