Modern nonlinear control theory seeks to endow systems with properties such as stability and safety, and has been deployed successfully across various domains. Despite this success, model uncertainty remains a significant challenge in ensuring that model-based controllers transfer to real world systems. This paper develops a data-driven approach to robust control synthesis in the presence of model uncertainty using Control Certificate Functions (CCFs), resulting in a convex optimization based controller for achieving properties like stability and safety. An important benefit of our framework is nuanced data-dependent guarantees, which in principle can yield sample-efficient data collection approaches that need not fully determine the input-to-state relationship. This work serves as a starting point for addressing important questions at the intersection of nonlinear control theory and non-parametric learning, both theoretical and in application. We validate the proposed method in simulation with an inverted pendulum in multiple experimental configurations.
This paper studies the control problem for safety-critical multi-agent systems based on quadratic programming (QP). Each controlled agent is modeled as a cascade connection of an integrator and an uncertain nonlinear actuation system. In particular, the integrator represents the position-velocity relation, and the actuation system describes the dynamic response of the actual velocity to the velocity reference signal. The notion of input-to-output stability (IOS) is employed to characterize the essential velocity-tracking capability of the actuation system. The uncertain actuation dynamics may …
This paper presents a nonlinear control algorithm for speed control of a permanent magnet motor. The idea relies on a feedback linearization technique which also ensures adherence to current and voltage bounds. These bounds arise from practical limitations of the power source. The feedback linearization law is computed using a convex optimization routine to minimize response time as well. The aid of convex optimization leads to computational efficiency. Moreover, the mathematical tractability of the approach also aids analysis of the system performance under model uncertainty and feedback meas…
Robotic tasks, like reaching a pre-grasp configuration, are specified in the end effector space or task space, whereas, robot motion is controlled in joint space. Because of inherent actuation errors in joint space, robots cannot achieve desired configurations in task space exactly. Furthermore, different inverse kinematics (IK) solutions map joint space error set to task space differently. Thus for a given task with a prescribed error tolerance, all IK solutions will not be guaranteed to successfully execute the task. Any IK solution that is guaranteed to execute a task (possibly with high pr…
The use of conventional actuators in robotic systems (electric motors in particular), while often offering advantages in terms of flexibility and controllability, suffer from primary actuator failure,due to unexpected complexities in their environment, which can lead to loss of controllability. Conventional actuators can impose disadvantages on mechanical complexity, weight, and cost. Here,the Mixed conventional/braking Actuation Mobile Robot (MAMR), a new mobile robot platform,is proposed to tackle such drawbacks in actuation and explore the use and control of braking actuation. This platform…
We present a novel class of nonlinear controllers that interpolates among differently behaving linear controllers as a case study for recently proposed Linear and Nonlinear System Level Synthesis framework. The structure of the nonlinear controller allows for simultaneously satisfying performance and safety objectives defined for small- and large-disturbance regimes. The proposed controller is distributed, handles delays, sparse actuation, and localizes disturbances. We show our nonlinear controller always outperforms its linear counterpart for constrained LQR problems. We further demonstrate …
Radboud University（拉德堡德大学）；University of Oxford（牛津大学）
Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability. However, the underlying models exclusively capture aleatoric but not epistemic uncertainty, and thus require that model parameters are known precisely. Our contribution to overcoming this restriction is a novel abstraction-based co…
Optimization Under Uncertainty for Energy Infrastructure Planning: A Synthesis of Methods, Tools, and Open Challenges
MIT Energy Initiative, MIT（麻省理工学院能源倡议）；Laboratory for Information and Decision Systems (LIDS), MIT（麻省理工学院信息与决策系统实验室）；Civil and Environmental Engineering (CEE), MIT（麻省理工学院土木与环境工程系）；Electrical Engineering and Computer Science (EECS), MIT（麻省理工学院电气与计算机工程系）
We consider the problem of how to deploy a controller to a (networked) cyber-physical system (CPS). Controlling a CPS is an involved task, and synthesizing a controller to respect sensing, actuation, and communication constraints is only part of the challenge. In addition to controller synthesis, one should also consider how the controller will be incorporated within the CPS. Put another way, the cyber layer and its interaction with the physical layer need to be taken into account. In this work, we aim to bridge the gap between theoretical controller synthesis and practical CPS deployment. We …
Grid-following and grid-forming inverters are integral components of microgrids and for integration of renewable energy sources with the grid. For grid following inverters, which need to emulate controllable current sources, a significant challenge is to address the large uncertainty of the grid impedance. For grid forming inverters, which need to emulate a controllable voltage source, large uncertainty due to varying loads has to be addressed. In this article, a mu-synthesis-based robust control design methodology, where performance under quantified uncertainty is guaranteed, is developed und…
Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning
Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气工程与计算机科学系）；Department of Computer Science, Johns Hopkins University（约翰霍普金斯大学计算机科学系）
We consider the problem of how to deploy a controller to a (networked) cyber-physical system (CPS). Controlling a CPS is an involved task, and synthesizing a controller to respect sensing, actuation, and communication constraints is only part of the challenge. In addition to controller synthesis, one should also consider how the controller will work in the CPS. Put another way, the cyber layer and its interaction with the physical layer need to be taken into account. In this work, we aim to bridge the gap between theoretical controller synthesis and practical CPS deployment. We adopt the syste…
Biological and advanced cyberphysical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new "system level" (SL) approach involving three complementary SL elements. System Level Parameterizations (SLPs) generalize state space and Youla parameterizations of all stabilizing controllers and the responses they ach…
We present a robust model predictive control method (MPC) for discrete-time linear time-delayed systems with state and control input constraints. The system is subject to both polytopic model uncertainty and additive disturbances. In the proposed method, a time-varying feedback control policy is optimized such that the robust satisfaction of all constraints for the closed-loop system is guaranteed. By encoding the effects of the delayed states and inputs into the feedback policy, we solve the robust optimal control problem in MPC using System Level Synthesis which results in a convex quadratic…
Sensor-Driven Mission Synthesis for UAV/UGV Swarms: A TB-CSPN Coordination Architecture with Hardware-Enforced Safety
Institute for Software Technology, University of the Bundeswehr Munich（慕尼黑联邦国防军大学软件技术研究所）；Department of Computer Science, Sapienza University of Rome（罗马大学计算机科学系）；SofTware And Knowledge Engineering Lab（软件与知识工程实验室）
California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory（喷气推进实验室）
We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning for robotic systems under uncertainty. The gPC-SCP method involves two steps. The first step is to derive a surrogate problem of \emph{deterministic} nonlinear optimal control (DNOC) with convex constraints by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem us…
Multi-objective Robust Strategy Synthesis for Interval Markov Decision Processes
Saarland University（萨尔兰大学）；State Key Laboratory of Computer Science, ISCAS（中国科学院计算技术研究所）；Department of Computer Science, University of Oxford（牛津大学计算机系）
An approach is presented for robustness analysis and quantum (unitary) control synthesis based on the classic method of averaging. The result is a multicriterion optimization competing the nominal (uncertainty-free) fidelity with a well known robustness measure: the size of an interaction (error) Hamiltonian, essentially the first term in the Magnus expansion of an interaction unitary. Combining this with the fact that the topology of the control landscape at high fidelity is determined by the null space of the nominal fidelity Hessian, we arrive at a new two-stage algorithm. Once the nominal …
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze stability under mostly-periodic timing with bounded uncertainty, a timing model typical for the implementation of controllers that were actually designed for strictly periodic execution. In contrast to existing work, we include the case of multiple sensors and actuators with individual timing uncertainty. Our approach is based on the discretization of a linea…
This paper addresses the end-to-end sample complexity bound for learning in closed loop the state estimator-based robust H2 controller for an unknown (possibly unstable) Linear Time Invariant (LTI) system, when given a fixed state-feedback gain. We build on the results from Ding et al. (1994) to bridge the gap between the parameterization of all state-estimators and the celebrated Youla parameterization. Refitting the expression of the relevant closed loop allows for the optimal linear observer problem given a fixed state feedback gain to be recast as a convex problem in the Youla parameter. T…
Robust controller synthesis attracts reviving research interest, driven by the rise of learning-based systems where uncertainty and perturbation are ubiquitous. Facing an uncertain situation, a robustly stabilizing controller should maintain stability while operating under a perturbed system deviating from its nominal specification. There have been numerous results for robust controller synthesis in multiple forms and with various goals, including mu-synthesis, robust primal-dual Youla, robust input-output, and robust system level parameterizations. However, their connections with one another …
