arXiv subjects

Keyou You

Publications and source records attributed to Keyou You.

At least 37 records · Page 2Linked to original sources

arXiv2025

Direct Adaptive Control of Grid-Connected Power Converters via Output-Feedback Data-Enabled Policy Optimization

Power electronic converters are becoming the main components of modern power systems due to the increasing integration of renewable energy sources. However, power converters may become unstable when interacting with the complex and time-varying power grid. In this paper, we propose an adaptive data-driven control method to stabilize power converters by using only online input-output data. Our contributions are threefold. First, we reformulate the output-feedback control problem as a state-feedback linear quadratic regulator (LQR) problem with a controllable non-minimal state, which can be constructed from past input-output signals. Second, we propose a data-enabled policy optimization (DeePO) method for this non-minimal realization to achieve efficient output-feedback adaptive control. Third, we use high-fidelity simulations to verify that the output-feedback DeePO can effectively stabilize grid-connected power converters and quickly adapt to the changes in the power grid.

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arXiv2024

Reliably Learn to Trim Multiparametric Quadratic Programs via Constraint Removal

In a wide range of applications, we are required to rapidly solve a sequence of convex multiparametric quadratic programs (mp-QPs) on resource-limited hardwares. This is a nontrivial task and has been an active topic for decades in control and optimization communities. Observe that the main computational cost of existing solution algorithms lies in addressing many linear inequality constraints, though their majority are redundant and removing them will not change the optimal solution. This work learns from the results of previously solved mp-QP(s), based on which we propose novel methods to reliably trim (unsolved) mp-QPs via constraint removal, and the trimmed mp-QPs can be much cheaper to solve. Then, we extend to trim mp-QPs of model predictive control (MPC) whose parameter vectors are sampled from linear systems. Importantly, both online and offline solved mp-QPs can be utilized to adaptively trim mp-QPs in the closed-loop system. We show that the number of linear inequalities in the trimmed mp-QP of MPC decreases to zero in a finite timestep, which also can be reduced by increasing offline computation. Finally, simulations are performed to demonstrate the efficiency of our trimming method in removing redundant constraints.

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arXiv2024

Linear Convergence of Data-Enabled Policy Optimization for Linear Quadratic Tracking

Data-enabled policy optimization (DeePO) is a newly proposed method to attack the open problem of direct adaptive LQR. In this work, we extend the DeePO framework to the linear quadratic tracking (LQT) with offline data. By introducing a covariance parameterization of the LQT policy, we derive a direct data-driven formulation of the LQT problem. Then, we use gradient descent method to iteratively update the parameterized policy to find an optimal LQT policy. Moreover, by revealing the connection between DeePO and model-based policy optimization, we prove the linear convergence of the DeePO iteration. Finally, a numerical experiment is given to validate the convergence results. We hope our work paves the way to direct adaptive LQT with online closed-loop data.

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arXiv2024

Data-Enabled Policy Optimization for Direct Adaptive Learning of the LQR

Direct data-driven design methods for the linear quadratic regulator (LQR) mainly use offline or episodic data batches, and their online adaptation has been acknowledged as an open problem. In this paper, we propose a direct adaptive method to learn the LQR from online closed-loop data. First, we propose a new policy parameterization based on the sample covariance to formulate a direct data-driven LQR problem, which is shown to be equivalent to the certainty-equivalence LQR with optimal non-asymptotic guarantees. Second, we design a novel data-enabled policy optimization (DeePO) method to directly update the policy, where the gradient is explicitly computed using only a batch of persistently exciting (PE) data. Third, we establish its global convergence via a projected gradient dominance property. Importantly, we efficiently use DeePO to adaptively learn the LQR by performing only one-step projected gradient descent per sample of the closed-loop system, which also leads to an explicit recursive update of the policy. Under PE inputs and for bounded noise, we show that the average regret of the LQR cost is upper-bounded by two terms signifying a sublinear decrease in time $\mathcal{O}(1/\sqrt{T})$ plus a bias scaling inversely with signal-to-noise ratio (SNR), which are independent of the noise statistics. Finally, we perform simulations to validate the theoretical results and demonstrate the computational and sample efficiency of our method.

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arXiv2024

Data-Driven Output Prediction and Control of Stochastic Systems: An Innovation-Based Approach

Recent years have witnessed a booming interest in data-driven control of dynamical systems. However, the implicit data-driven output predictors are vulnerable to uncertainty such as process disturbance and measurement noise, causing unreliable predictions and unexpected control actions. In this brief, we put forward a new data-driven approach to output prediction of stochastic linear time-invariant (LTI) systems. By utilizing the innovation form, the uncertainty in stochastic LTI systems is recast as innovations that can be readily estimated from input-output data without knowing system matrices. In this way, by applying the fundamental lemma to the innovation form, we propose a new innovation-based data-driven output predictor (OP) of stochastic LTI systems, which bypasses the need for identifying state-space matrices explicitly and building a state estimator. The boundedness of the second moment of prediction errors in closed-loop is established under mild conditions. The proposed data-driven OP can be integrated into optimal control design for better performance. Numerical simulations demonstrate the outperformance of the proposed innovation-based methods in output prediction and control design over existing formulations.

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arXiv2024

Asynchronous Parallel Policy Gradient Methods for the Linear Quadratic Regulator

Learning policies in an asynchronous parallel way is essential to the numerous successes of RL for solving large-scale problems. However, their convergence performance is still not rigorously evaluated. To this end, we adopt the asynchronous parallel zero-order policy gradient (AZOPG) method to solve the continuous-time linear quadratic regulation problem. Specifically, as in the celebrated A3C algorithm, there are multiple parallel workers to asynchronously estimate PGs which are then sent to a central master for policy updates. Via quantifying its convergence rate of policy iterations, we show the linear speedup property of the AZOPG, both in theory and simulation, which clearly reveals the advantages of using parallel workers for learning policies.

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arXiv2024

Policy Gradient Methods for the Cost-Constrained LQR: Strong Duality and Global Convergence

In safety-critical applications, reinforcement learning (RL) needs to consider safety constraints. However, theoretical understandings of constrained RL for continuous control are largely absent. As a case study, this paper presents a cost-constrained LQR formulation, where a number of LQR costs with user-defined penalty matrices are subject to constraints. To solve it, we propose a policy gradient primal-dual method to find an optimal state feedback gain. Despite the non-convexity of the cost-constrained LQR problem, we provide a constructive proof for strong duality and a geometric interpretation of an optimal multiplier set. By proving that the concave dual function is Lipschitz smooth, we further provide convergence guarantees for the PG primal-dual method. Finally, we perform simulations to validate our theoretical findings.

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arXiv2024

Harnessing Data for Accelerating Model Predictive Control by Constraint Removal

Model predictive control (MPC) solves a receding-horizon optimization problem in real-time, which can be computationally demanding when there are thousands of constraints. To accelerate online computation of MPC, we utilize data to adaptively remove the constraints while maintaining the MPC policy unchanged. Specifically, we design the removal rule based on the Lipschitz continuity of the MPC policy. This removal rule can use the information of historical data according to the Lipschitz constant and the distance between the current state and historical states. In particular, we provide the explicit expression for calculating the Lipschitz constant by the model parameters. Finally, simulations are performed to validate the effectiveness of the proposed method.

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arXiv2023

Distributed Adaptive Greedy Quasi-Newton Methods with Explicit Non-asymptotic Convergence Bounds

Though quasi-Newton methods have been extensively studied in the literature, they either suffer from local convergence or use a series of line searches for global convergence which is not acceptable in the distributed setting. In this work, we first propose a line search free greedy quasi-Newton (GQN) method with adaptive steps and establish explicit non-asymptotic bounds for both the global convergence rate and local superlinear rate. Our novel idea lies in the design of multiple greedy quasi-Newton updates, which involves computing Hessian-vector products, to control the Hessian approximation error, and a simple mechanism to adjust stepsizes to ensure the objective function improvement per iterate. Then, we extend it to the master-worker framework and propose a distributed adaptive GQN method whose communication cost is comparable with that of first-order methods, yet it retains the superb convergence property of its centralized counterpart. Finally, we demonstrate the advantages of our methods via numerical experiments.

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arXiv2023

Data-enabled Policy Optimization for the Linear Quadratic Regulator

Policy optimization (PO), an essential approach of reinforcement learning for a broad range of system classes, requires significantly more system data than indirect (identification-followed-by-control) methods or behavioral-based direct methods even in the simplest linear quadratic regulator (LQR) problem. In this paper, we take an initial step towards bridging this gap by proposing the data-enabled policy optimization (DeePO) method, which requires only a finite number of sufficiently exciting data to iteratively solve the LQR problem via PO. Based on a data-driven closed-loop parameterization, we are able to directly compute the policy gradient from a batch of persistently exciting data. Next, we show that the nonconvex PO problem satisfies a projected gradient dominance property by relating it to an equivalent convex program, leading to the global convergence of DeePO. Moreover, we apply regularization methods to enhance certainty-equivalence and robustness of the resulting controller and show an implicit regularization property. Finally, we perform simulations to validate our results.

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arXiv2023

Convergence and Sample Complexity of Policy Gradient Methods for Stabilizing Linear Systems

System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant systems in terms of the number of system rollouts. Our analysis is built upon a discounted linear quadratic regulator (LQR) method which alternatively updates the policy and the discount factor of the LQR problem. Firstly, we propose an explicit rule to adaptively adjust the discount factor by exploring the stability margin of a linear control policy. Then, we establish the sample complexity of PG methods for stabilization, which only adds a coefficient logarithmic in the spectral radius of the state matrix to that for solving the LQR problem with a prior stabilizing policy. Finally, we perform simulations to validate our theoretical findings and demonstrate the effectiveness of our method on a class of nonlinear systems.

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arXiv2023

Globally Convergent Policy Gradient Methods for Linear Quadratic Control of Partially Observed Systems

While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to stationary points. In this paper, we propose a new policy parameterization for partially observed linear systems, using a past input-output trajectory of finite length as feedback. We show that the solution set to the parameterized optimization problem is a matrix space, which is invariant to similarity transformation. By proving a gradient dominance property, we show the global convergence of policy gradient methods. Moreover, we observe that the gradient is orthogonal to the solution set, revealing an explicit relation between the resulting solution and the initial policy. Finally, we perform simulations to validate our theoretical results.

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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

Standoff Tracking Using DNN-Based MPC with Implementation on FPGA

This work studies the standoff tracking problem to drive an unmanned aerial vehicle (UAV) to slide on a desired circle over a moving target at a constant height. We propose a novel Lyapunov guidance vector (LGV) field with tunable convergence rates for the UAV's trajectory planning and a deep neural network (DNN)-based model predictive control (MPC) scheme to track the reference trajectory. Then, we show how to collect samples for training the DNN offline and design an integral module (IM) to refine the tracking performance of our DNN-based MPC. Moreover, the hardware-in-the-loop (HIL) simulation with an FPGA@200MHz demonstrates that our method is a valid alternative to embedded implementations of MPC for addressing complex systems and applications which is impossible for directly solving the MPC optimization problems.

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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

Quantized Distributed Gradient Tracking Algorithm with Linear Convergence in Directed Networks

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this paper proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive the update rule for the number of quantization levels, and prove that Q-DGT can converge linearly even when the exchanged variables are respectively one bit. Numerical results also confirm the efficiency of the proposed algorithm.

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arXiv2022

Optimal $(0,1)$-Matrix Completion with Majorization Ordered Objectives (To the memory of Pravin Varaiya)

We propose and examine two optimal $(0,1)$-matrix completion problems with majorization ordered objectives. They elevate the seminal study by Gale and Ryser from feasibility to optimality in partial order programming (POP), referring to optimization with partially ordered objectives. We showcase their applications in electric vehicle charging, portfolio optimization, and secure data storage. Solving such integer POP (iPOP) problems is challenging because of the possible non-comparability among objective values and the integer requirements. Nevertheless, we prove the essential uniqueness of all optimal objective values and identify two particular ones for each of the two inherently symmetric iPOP problems. Furthermore, for every optimal objective value, we decompose the construction of an associated optimal~$(0,1)$-matrix into a series of sorting processes, respectively agreeing with the rule of thumb "peak shaving" or "valley filling." We show that the resulting algorithms have linear time complexities and verify their empirical efficiency via numerical simulations compared to the standard order-preserving method for POP.

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arXiv2022

Minimum Input Design for Direct Data-driven Property Identification of Unknown Linear Systems

In a direct data-driven approach, this paper studies the {\em property identification(ID)} problem to analyze whether an unknown linear system has a property of interest, e.g., stabilizability and structural properties. In sharp contrast to the model-based analysis, we approach it by directly using the input and state feedback data of the unknown system. Via a new concept of sufficient richness of input sectional data, we first establish the necessary and sufficient condition for the minimum input design to excite the system for property ID. Specifically, the input sectional data is sufficiently rich for property ID {\em if and only if} it spans a linear subspace that contains a property dependent minimum linear subspace, any basis of which can also be easily used to form the minimum excitation input. Interestingly, we show that many structural properties can be identified with the minimum input that is however unable to identify the explicit system model. Overall, our results rigorously quantify the advantages of the direct data-driven analysis over the model-based analysis for linear systems in terms of data efficiency.

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