arXiv subjects

Feiran Zhao

Publications and source records attributed to Feiran Zhao.

26 records · Page 2Linked to original sources

arXiv2023

Minimax Q-learning Control for Linear Systems Using the Wasserstein Metric

Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear systems and adopt a Wasserstein penalty to address the distribution uncertainty of additive stochastic disturbances. By constructing an equivalent deterministic game of the penalized LQR problem, we propose a Q-learning method with convergence guarantees to learn an optimal minimax controller.

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arXiv2022

Global Convergence of Policy Gradient Primal-dual Methods for Risk-constrained LQRs

While the techniques in optimal control theory are often model-based, the policy optimization (PO) approach directly optimizes the performance metric of interest. Even though it has been an essential approach for reinforcement learning problems, there is little theoretical understanding on its performance. In this paper, we focus on the risk-constrained linear quadratic regulator (RC-LQR) problem via the PO approach, which requires addressing a challenging non-convex constrained optimization problem. To solve it, we first build on our earlier result that an optimal policy has a time-invariant affine structure to show that the associated Lagrangian function is coercive, locally gradient dominated and has local Lipschitz continuous gradient, based on which we establish strong duality. Then, we design policy gradient primal-dual methods with global convergence guarantees in both model-based and sample-based settings. Finally, we use samples of system trajectories in simulations to validate our methods.

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arXiv2022

System-Level Evaluation of Beam Hopping in NR-Based LEO Satellite Communication System

Satellite communication by leveraging the use of low earth orbit (LEO) satellites is expected to play an essential role in future communication systems through providing ubiquitous and continuous wireless connectivity. This thus has motivated the work in the 3rd generation partnership project (3GPP) to ensure the operation of fifth generation (5G) New Radio (NR) protocols for non-terrestrial network (NTN). In this paper, we consider a NR-based LEO satellite communication system, where satellites equipped with phased array antennas are employed to serve user equipments (UEs) on the ground. To reduce payload weight and meet the time-varying traffic demands of UEs, an efficient beam hopping scheme considering both the traffic demands and inter-beam interference is proposed to jointly schedule beams and satellite transmit power. Then based on NR protocols, we present the first system-level evaluations of beam hopping scheme in LEO satellite system under different operating frequency bands and traffic models. Simulation results indicate that significant performance gains can be achieved by the proposed beam hopping scheme, especially under the distance limit constraint that avoids scheduling adjacent beams simultaneously, as compared to benchmark schemes.

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arXiv2022

Data-driven Control of Unknown Linear Systems via Quantized Feedback

Control using quantized feedback is a fundamental approach to system synthesis with limited communication capacity. In this paper, we address the stabilization problem for unknown linear systems with logarithmically quantized feedback, via a direct data-driven control method. By leveraging a recently developed matrix S-lemma, we prove a sufficient and necessary condition for the existence of a common stabilizing controller for all possible dynamics consistent with data, in the form of a linear matrix inequality. Moreover, we formulate semi-definite programming to solve the coarsest quantization density. By establishing its connections to unstable eigenvalues of the state matrix, we further prove a necessary rank condition on the data for quantized feedback stabilization. Finally, we validate our theoretical results by numerical examples.

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arXiv2021

Learning Stabilizing Controllers of Linear Systems via Discount Policy Gradient

Stability is one of the most fundamental requirements for systems synthesis. In this paper, we address the stabilization problem for unknown linear systems via policy gradient (PG) methods. We leverage a key feature of PG for Linear Quadratic Regulator (LQR), i.e., it drives the policy away from the boundary of the unstabilizing region along the descent direction, provided with an initial policy with finite cost. To this end, we discount the LQR cost with a factor, by adaptively increasing which gradient leads the policy to the stabilizing set while maintaining a finite cost. Based on the Lyapunov theory, we design an update rule for the discount factor which can be directly computed from data, rendering our method purely model-free. Compared to recent work \citep{perdomo2021stabilizing}, our algorithm allows the policy to be updated only once for each discount factor. Moreover, the number of sampled trajectories and simulation time for gradient descent is significantly reduced to $\mathcal{O}(\log(1/ε))$ for the desired accuracy $ε$. Finally, we conduct simulations on both small-scale and large-scale examples to show the efficiency of our discount PG method.

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arXiv2021

Primal-dual Learning for the Model-free Risk-constrained Linear Quadratic Regulator

Risk-aware control, though with promise to tackle unexpected events, requires a known exact dynamical model. In this work, we propose a model-free framework to learn a risk-aware controller with a focus on the linear system. We formulate it as a discrete-time infinite-horizon LQR problem with a state predictive variance constraint. To solve it, we parameterize the policy with a feedback gain pair and leverage primal-dual methods to optimize it by solely using data. We first study the optimization landscape of the Lagrangian function and establish the strong duality in spite of its non-convex nature. Alongside, we find that the Lagrangian function enjoys an important local gradient dominance property, which is then exploited to develop a convergent random search algorithm to learn the dual function. Furthermore, we propose a primal-dual algorithm with global convergence to learn the optimal policy-multiplier pair. Finally, we validate our results via simulations.

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arXiv2021

Infinite-horizon Risk-constrained Linear Quadratic Regulator with Average Cost

The behaviour of a stochastic dynamical system may be largely influenced by those low-probability, yet extreme events. To address such occurrences, this paper proposes an infinite-horizon risk-constrained Linear Quadratic Regulator (LQR) framework with time-average cost. In addition to the standard LQR objective, the average one-stage predictive variance of the state penalty is constrained to lie within a user-specified level. By leveraging the duality, its optimal solution is first shown to be stationary and affine in the state, i.e., $u(x,λ^*) = -K(λ^*)x + l(λ^*)$, where $λ^*$ is an optimal multiplier, used to address the risk constraint. Then, we establish the stability of the resulting closed-loop system. Furthermore, we propose a primal-dual method with sublinear convergence rate to find an optimal policy $u(x,λ^*)$. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed framework and the primal-dual method.

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arXiv2020

Suspension Regulation of Medium-low-speed Maglev Trains via Deep Reinforcement Learning

The suspension regulation is critical to the operation of medium-low-speed maglev trains (mlsMTs). Due to uncertain environment, strong disturbances and high nonlinearity of the system dynamics, this problem cannot be well solved by most of the model-based controllers. In this paper, we propose a model-free controller by reformulating it as a continuous-state, continuous-action Markov decision process (MDP) with unknown transition probabilities. With the deterministic policy gradient and neural network approximation, we design reinforcement learning (RL) algorithms to solve the MDP and obtain a state-feedback controller by using sampled data from the suspension system. To further improve its performance, we adopt a double Q-learning scheme for learning the regulation controller. We illustrate that the proposed controllers outperform the existing PID controller with a real dataset from the mlsMT in Changsha, China and is even comparable to model-based controllers, which assume that the complete information of the model is known, via simulations.

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