| 1. |
- Gao, Yulong, et al.
(författare)
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Computing Probabilistic Controlled Invariant Sets
- 2021
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Ingår i: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 66:7, s. 3138-3151
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Tidskriftsartikel (refereegranskat)abstract
- This article investigates stochastic invariance for control systems through probabilistic controlled invariant sets (PCISs). As a natural complement to robust controlled invariant sets (RCISs), we propose finite-, and infinite-horizon PCISs, and explore their relation to RICSs. We design iterative algorithms to compute the PCIS within a given set. For systems with discrete spaces, the computations of the finite-, and infinite-horizon PCISs at each iteration are based on linear programming, and mixed integer linear programming, respectively. The algorithms are computationally tractable, and terminate in a finite number of steps. For systems with continuous spaces, we show how to discretize the spaces, and prove the convergence of the approximation when computing the finite-horizon PCISs. In addition, it is shown that an infinite-horizon PCIS can be computed by the stochastic backward reachable set from the RCIS contained in it. These PCIS algorithms are applicable to practical control systems. Simulations are given to illustrate the effectiveness of the theoretical results for motion planning.
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| 2. |
- Gao, Yulong, et al.
(författare)
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Distributed Freeway Ramp Metering : Optimization on Flow Speed
- 2017
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Ingår i: 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. - : IEEE. - 9781509028733
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Konferensbidrag (refereegranskat)abstract
- This paper studies the distributed freeway ramp metering problem, for which the cell transmission model (CTM) is utilized. Considering the jam density and the upper bounds on the queue lengths and the ramp metering, we first provide feasibility conditions with respect to the external demand to ensure the controllability of the freeway. Assuming that the freeway is controllable, we formulate an optimization problem which tradeoffs the maximum average flow speed and the minimum waiting queue for each cell. Although the cells of the CTM are dynamically coupled, we propose a distributed backward algorithm for the optimization problem and prove that the solution to the problem is a Nash equilibrium. Furthermore, if the optimization problem is simplified to only maximization of the average flow speed, we argue that the obtained explicit distributed controller is globally optimal. A numerical example is given to illustrate the effectiveness of the proposed control algorithm.
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| 3. |
- Gao, Yulong, et al.
(författare)
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Distributional Reachability for Markov Decision Processes : Theory and Applications
- 2024
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 69:7, s. 4598-4613
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Tidskriftsartikel (refereegranskat)abstract
- We study distributional reachability for finite Markov decision processes (MDPs) from a control theoretical perspective. Unlike standard probabilistic reachability notions, which are defined over MDP states or trajectories, in this paper reachability is formulated over the space of probability distributions. We propose two set-valued maps for the forward and backward distributional reachability problems: the forward map collects all state distributions that can be reached from a set of initial distributions, while the backward map collects all state distributions that can reach a set of final distributions. We show that there exists a maximal invariant set under the forward map and this set is the region where the state distributions eventually always belong to, regardless of the initial state distribution and policy. The backward map provides an alternative way to solve a class of important problems for MDPs: the study of controlled invariance, the characterization of the domain of attraction, and reach-avoid problems. Three case studies illustrate the effectiveness of our approach.
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| 4. |
- Gao, Yulong, et al.
(författare)
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Invariant cover : Existence, cardinality bounds, and computation
- 2021
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Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 129
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Tidskriftsartikel (refereegranskat)abstract
- An invariant cover quantifies the information needed by a controller to enforce an invariance specification. This paper investigates some fundamental problems concerning existence and computation of an invariant cover for uncertain discrete-time linear control systems subject to state and control constraints. We develop necessary and sufficient conditions on the existence of an invariant cover for a polytopic set of states. The conditions can be checked by solving a set of linear programs, one for each extreme point of the state set. Based on these conditions, we give upper and lower bounds on the minimal cardinality of the invariant cover, and design an iterative algorithm with finite-time convergence to compute an invariant cover. We further show in two examples how to use an invariant cover in the design of a coder-controller pair that ensures invariance of a given set for a networked control system with a finite communication data rate.
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| 5. |
- Gao, Yulong, et al.
(författare)
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Reachability-based Human-in-the-Loop Control with Uncertain Specifications
- 2020
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Ingår i: IFAC PAPERSONLINE. - : Elsevier BV. - 2405-8963. ; , s. 1880-1887
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Konferensbidrag (refereegranskat)abstract
- We propose a shared autonomy approach for implementing human operator decisions onto an automated system during multi-objective missions, while guaranteeing safety and mission completion. A mission is specified as a set of linear temporal logic (LTL) formulae. Then, using a novel correspondence between LTL and reachability analysis, we synthesize a set of controllers for assisting the human operator to complete the mission, while guaranteeing that the system maintains specified spatial and temporal properties. We assume the human operator's exact preference of how to complete the mission is unknown. Instead, we use a datadriven approach to infer and update the automated system's internal belief of which specified objective the human intends to complete. If, while the human is operating the system, she provides inputs that violate any of the invariances prescribed by the LTL formula, our verified controller will use its internal belief of the human operator's intended objective to guide the operator back on track. Moreover, we show that as long as the specifications are initially feasible, our controller will stay feasible and can guide the human to complete the mission despite some unexpected human errors. We illustrate our approach with a simple, but practical, experimental setup where a remote operator is parking a vehicle in a parking lot with multiple parking options. In these experiments, we show that our approach is able to infer the human operator's preference over parking spots in real-time and guarantee that the human will park in the spot safely.
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| 6. |
- Gao, Yulong, et al.
(författare)
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Robust self-triggered control for time-varying and uncertain constrained systems via reachability analysis
- 2019
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Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 107, s. 574-581
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Tidskriftsartikel (refereegranskat)abstract
- This paper develops a robust self-triggered control algorithm for time-varying and uncertain systems with constraints based on reachability analysis. The resulting piecewise constant control inputs achieve communication reduction and guarantee constraint satisfactions. In the particular case when there is no uncertainty, we propose a control design with minimum number of samplings over finite time horizon. Furthermore, when the plant is linear and the constraints are polyhedral, we prove that the previous algorithms can be reformulated as computationally tractable mixed integer linear programs. The method is compared with the robust self-triggered model predictive control in a numerical example and applied to a robot motion planning problem with temporal constraints.
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| 7. |
- Gao, Yulong, 1990-
(författare)
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Safe Autonomy under Uncertainty: Computation, Control, and Application
- 2020
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Safety is a primary requirement for many autonomous systems, such as automated vehicles and mobile robots. An open problem is how to assure safety, in the sense of avoiding unsafe subsets of the state space, for uncertain systems under complex tasks. In this thesis, we solve this problem for certain system classes and uncertainty descriptions by developing computational tools, designing verification and control synthesis algorithms, and evaluating them on two applications.As our first contribution, we consider how to compute probabilistic controlled invariant sets, which are sets the controller is able to keep the system state within with a certain probability. By using stochastic backward reachability, we design algorithms to compute these sets. We prove that the algorithms are computationally tractable and converge in a finite number of iterations. We further consider how to compute invariant covers, which are covers of sets that can be enforced to be invariant by a finite number of control inputs despite disturbances.A necessary and sufficient condition on the existence of an invariant cover is derived. Based on this result, an efficient computational algorithm is designed.The second contribution is to develop algorithms for model checking and control synthesis. We consider discrete-time uncertain systems under linear temporal logic (LTL) specifications. We propose the new notion of temporal logic trees (TLT) and show how to construct TLT from LTL formulae via reachability analysis for both autonomous and controlled transition systems. We prove approximation relations between TLT and LTL formulae. Two sufficient conditions are given to verify whether a transition system satisfies an LTL formula. An online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step, is designed, and it is proven to be recursively feasible.As our third contribution, we study two important vehicular applications on shared-autonomy systems, which are systems with a mix of human and automated decisions. For the first application, we consider a car parking problem, where a remote human operator is guided to drive a vehicle to an empty parking spot. An automated controller is designed to guarantee safety and mission completion despite unpredictable human actions. For the second application, we consider a car overtaking problem, where an automated vehicle overtakes a human-driven vehicle with uncertain motion. We design a risk-aware optimal overtaking algorithm with guaranteed levels of safety.
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| 8. |
- Gao, Yulong, et al.
(författare)
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Stochastic Optimal Control of Dynamic Queue Systems : A Probabilistic Perspective
- 2018
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Ingår i: 2018 15TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION, ROBOTICS AND VISION (ICARCV). - : IEEE. - 9781538695821 ; , s. 837-842
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Konferensbidrag (refereegranskat)abstract
- Queue overflow of a dynamic queue system gives rise to the information loss (or packet loss) in the communication buffer or the decrease of throughput in the transportation network. This paper investigates a stochastic optimal control problem for dynamic queue systems when imposing probability constraints on queue overflows. We reformulate this problem as a Markov decision process (MDP) with safety constraints. We prove that both finite-horizon and infinite-horizon stochastic optimal control for MDP with such constraints can be transformed as a linear program (LP), respectively. Feasibility conditions are provided for the finite-horizon constrained control problem. Two implementation algorithms are designed under the assumption that only the state (not the state distribution) can be observed at each time instant. Simulation results compare optimal cost and state distribution among different scenarios, and show the probability constraint satisfaction by the proposed algorithms.
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| 9. |
- Gao, Yulong, et al.
(författare)
-
Temporal Logic Trees for Model Checking and Control Synthesis of Uncertain Discrete-time Systems
- 2021
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; , s. 1-1
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Tidskriftsartikel (refereegranskat)abstract
- We propose algorithms for performing model checking and control synthesis for discrete-time uncertain systems under linear temporal logic (LTL) specifications. We construct temporal logic trees (TLT) from LTL formulae via reachability analysis. In contrast to automaton-based methods, the construction of the TLT is abstraction-free for infinite systems, that is, we do not construct discrete abstractions of the infinite systems. Moreover, for a given transition system and an LTL formula, we prove that there exist both a universal TLT and an existential TLT via minimal and maximal reachability analysis, respectively. We show that the universal TLT is an underapproximation for the LTL formula and the existential TLT is an overapproximation. We provide sufficient conditions and necessary conditions to verify whether a transition system satisfies an LTL formula by using the TLT approximations. As a major contribution of this work, for a controlled transition system and an LTL formula, we prove that a controlled TLT can be constructed from the LTL formula via control-dependent reachability analysis. Based on the controlled TLT, we design an online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step. We also prove that this algorithm is recursively feasible. We illustrate the proposed methods for both finite and infinite systems and highlight the generality and online scalability with two simulated examples.
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| 10. |
- Han, Duo, et al.
(författare)
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Optimal Parameter Estimation Under Controlled Communication Over Sensor Networks
- 2015
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Ingår i: IEEE Transactions on Signal Processing. - : IEEE. - 1053-587X .- 1941-0476. ; 63:24, s. 6473-6485
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers parameter estimation of linear systems under sensor-to-estimator communication constraint. Due to the limited battery power and the traffic congestion over a large sensor network, each sensor is required to reduce the rate of communication between the estimator and itself. We propose an observation-driven sensor scheduling policy such that the sensor transmits only the important measurements to the estimator. Unlike the existing deterministic scheduler, our stochastic scheduling is smartly designed to well compensate for the loss of the Gaussianity of the system. This results in a nice feature that the maximum-likelihood estimator (MLE) is still able to be recursively computed in a closed form, and the resulting estimation performance can be explicitly evaluated. Moreover, an optimization problem is formulated and solved to obtain the best parameters of the scheduling policy under which the estimation performance becomes comparable to the standard MLE with full measurements under a moderate transmission rate. Finally, simulations are included to validate the theoretical results.
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