arXiv subjects

Zheng-Guang Wu

Publications and source records attributed to Zheng-Guang Wu.

5 recordsLinked to original sources

arXiv2024

Distributed Adaptive Time-Varying Optimization with Global Asymptotic Convergence

In this note, we study distributed time-varying optimization for a multi-agent system. We first focus on a class of time-varying quadratic cost functions, and develop a new distributed algorithm that integrates an average estimator and an adaptive optimizer, with both bridged by a Dead Zone Algorithm. Based on a composite Lyapunov function and finite escape-time analysis, we prove the closed-loop global asymptotic convergence to the optimal solution under mild assumptions. Particularly, the introduction of the estimator relaxes the requirement for the Hessians of cost functions, and the integrated design eliminates the waiting time required in the relevant literature for estimating global parameter during algorithm implementation. We then extend this result to a more general class of time-varying cost functions. Two examples are used to verify the proposed designs.

eess.SY↗

arXiv2024

Distributed Continuous-Time Optimization with Uncertain Time-Varying Quadratic Cost Functions

This paper studies distributed continuous-time optimization for time-varying quadratic cost functions with uncertain parameters. We first propose a centralized adaptive optimization algorithm using partial information of the cost function. It can be seen that even if there are uncertain parameters in the cost function, exact optimization can still be achieved. To solve this problem in a distributed manner when different local cost functions have identical Hessians, we propose a novel distributed algorithm that cascades the fixed-time average estimator and the distributed optimizer. We remove the requirement for the upper bounds of certain complex functions by integrating state-based gains in the proposed design. We further extend this result to address the distributed optimization where the time-varying cost functions have nonidentical Hessians. We prove the convergence of all the proposed algorithms in the global sense. Numerical examples verify the proposed algorithms.

eess.SY↗

arXiv2023

Deep Reinforcement Learning Based Optimal Infinite-Horizon Control of Probabilistic Boolean Control Networks

In this paper, a deep reinforcement learning based method is proposed to obtain optimal policies for optimal infinite-horizon control of probabilistic Boolean control networks (PBCNs). Compared with the existing literatures, the proposed method is model-free, namely, the system model and the initial states needn't to be known. Meanwhile, it is suitable for large-scale PBCNs. First, we establish the connection between deep reinforcement learning and optimal infinite-horizon control, and structure the problem into the framework of the Markov decision process. Then, PBCNs are defined as large-scale or small-scale, depending on whether the memory of the action-values exceeds the RAM of the computer. Based on the newly introduced definition, Q-learning (QL) and double deep Q-network (DDQN) are applied to the optimal infinite-horizon control of small-scale and large-scale PBCNs, respectively. Meanwhile, the optimal state feedback controllers are designed. Finally, two examples are presented, which are a small-scale PBCN with 3 nodes, and a large-scale one with 28 nodes. To verify the convergence of QL and DDQN, the optimal control policy and the optimal action-values, which are obtained from both the algorithms, are compared with the ones based on a model-based method named policy iteration. Meanwhile, the performance of QL is compared with DDQN in the small-scale PBCN.

eess.SY↗

arXiv2022

Robust optimization for quantum reinforcement learning control using partial observations

The current quantum reinforcement learning control models often assume that the quantum states are known a priori for control optimization. However, full observation of quantum state is experimentally infeasible due to the exponential scaling of the number of required quantum measurements on the number of qubits. In this paper, we investigate a robust reinforcement learning method using partial observations to overcome this difficulty. This control scheme is compatible with near-term quantum devices, where the noise is prevalent and predetermining the dynamics of quantum state is practically impossible. We show that this simplified control scheme can achieve similar or even better performance when compared to the conventional methods relying on full observation. We demonstrate the effectiveness of this scheme on examples of quantum state control and quantum approximate optimization algorithm. It has been shown that high-fidelity state control can be achieved even if the noise amplitude is at the same level as the control amplitude. Besides, an acceptable level of optimization accuracy can be achieved for QAOA with noisy control Hamiltonian. This robust control optimization model can be trained to compensate the uncertainties in practical quantum computing.

quant-ph↗

arXiv2020

Distributed Averaging Problems over Directed Signed Networks

This paper aims at addressing distributed averaging problems for signed networks in the presence of general directed topologies that are represented by signed digraphs. A new class of improved Laplacian potential functions is proposed by presenting two notions of any signed digraph: induced unsigned digraph and mirror (undirected) signed graph, based on which two distributed averaging protocols are designed using the nearest neighbor rules. It is shown that with any of the designed protocols, signed-average consensus (respectively, state stability) can be achieved if and only if the associated signed digraph of signed network is structurally balanced (respectively, unbalanced), regardless of whether weight balance is satisfied or not. Further, improved Laplacian potential functions can be exploited to solve fixed-time consensus problems of signed networks with directed topologies, in which a nonlinear distributed protocol is proposed to ensure the bipartite consensus or state stability within a fixed time. Additionally, the convergence analyses of directed signed networks can be implemented with the Lyapunov stability analysis method, which is realized by revealing the tight relationship between convergence behaviors of directed signed networks and properties of improved Laplacian potential functions. Illustrative examples are presented to demonstrate the validity of our theoretical results for directed signed networks.

math.OC↗