Jingfan Zhang

Bio: Jingfan Zhang is an academic researcher from University of Manchester. The author has contributed to research in topics: Multiplier (Fourier analysis) & Finite impulse response. The author has an hindex of 4, co-authored 11 publications receiving 39 citations.

Learning-Based Balance Control of Wheel-Legged Robots

Abstract: This letter studies the adaptive optimal control problem for a wheel-legged robot in the absence of an accurate dynamic model. A crucial strategy is to exploit recent advances in reinforcement learning (RL) and adaptive dynamic programming (ADP) to derive a learning-based solution to adaptive optimal control. It is shown that suboptimal controllers can be learned directly from input-state data collected along the trajectories of the robot. Rigorous proofs for the convergence of the novel data-driven value iteration (VI) algorithm and the stability of the closed-loop robot system are provided. Experiments are conducted to demonstrate the efficiency of the novel adaptive suboptimal controller derived from the data-driven VI algorithm in balancing the wheel-legged robot to the equilibrium.

Balance Control of a Novel Wheel-legged Robot: Design and Experiments

Abstract: This paper presents a balance control technique for a novel wheel-legged robot. We first derive a dynamic model of the robot and then apply a linear feedback controller based on output regulation and linear quadratic regulator (LQR) methods to maintain the standing of the robot on the ground without moving backward and forward mightily. To take into account nonlinearities of the model and obtain a large domain of stability, a nonlinear controller based on the interconnection and damping assignment - passivity-based control (IDA-PBC) method is exploited to control the robot in more general scenarios. Physical experiments are performed with various control tasks. Experimental results demonstrate that the proposed linear output regulator can maintain the standing of the robot, while the proposed nonlinear controller can balance the robot under an initial starting angle far away from the equilibrium point, or under a changing robot height.

Convex Searches for Discrete-Time Zames–Falb Multipliers

Abstract: In this article, we develop and analyze convex searches for Zames–Falb multipliers. We present two different approaches: infinite impulse response (IIR) and finite impulse response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large-order FIR multiplier. We show that searches in discrete time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell _{2}$ -stability results in the literature for slope-restricted nonlinearities. In particular, we establish the equivalence between the state-of-the-art Lyapunov results for slope-restricted nonlinearities and a subset of the FIR multipliers. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.

Absolute Stability of Systems With Integrator and/or Time Delay via Off-Axis Circle Criterion

Abstract: Graphical methods are a key tool to analyze Lur’e systems with time delay. In this letter we revisit clockwise properties of the Nyquist plot and extend results in the literature to critically stable systems and time-delayed systems. It is known that rational transfer functions with no resonant poles and no zeros satisfy the Kalman conjecture. We show that the same class of transfer functions in series with a time delay also satisfies the Kalman conjecture. Furthermore the same class of transfer functions in series with an integrator and delay (which may be zero) satisfies a suitably relaxed form of the Kalman conjecture. Useful results are also obtained where the delay is constant but unknown. Results in this letter can be used as benchmarks to test sufficient stability conditions for the Lur’e problem with time-delay systems.

Kalman Conjecture for Resonant Second-Order Systems with Time Delay

Abstract: We construct Zames-Falb multipliers for second-order systems with time delay. There are at least two equality constraints on the multiplier phase in the limiting case as the damping ratio tends to zero and the gain approaches the Nyquist gain. Nevertheless we demonstrate a multiplier exists for every system we consider. Our results depend on numerical examples and searches; thus while the Kalman Conjecture is apparently verified for this class of system, a formal proof is beyond the scope of the paper.

Robust and structure exploiting optimisation algorithms: an integral quadratic constraint approach

Abstract: We consider the problem of analysing and designing gradient-based discrete-time optimisation algorithms for a class of unconstrained optimisation problems having strongly convex objective functions...

A Robust Accelerated Optimization Algorithm for Strongly Convex Functions

Abstract: This work proposes an accelerated first-order algorithm we call the Robust Momentum Method for optimizing smooth strongly convex functions. The algorithm has a single scalar parameter that can be tuned to trade off robustness to gradient noise versus worst-case convergence rate. At one extreme, the algorithm is faster than Nesterov's Fast Gradient Method by a constant factor but more fragile to noise. At the other extreme, the algorithm reduces to the Gradient Method and is very robust to noise. The algorithm design technique is inspired by methods from classical control theory and the resulting algorithm has a simple analytical form. Algorithm performance is verified on a series of numerical simulations in both noise-free and relative gradient noise cases.

Learning-Based Balance Control of Wheel-Legged Robots

Abstract: This letter studies the adaptive optimal control problem for a wheel-legged robot in the absence of an accurate dynamic model. A crucial strategy is to exploit recent advances in reinforcement learning (RL) and adaptive dynamic programming (ADP) to derive a learning-based solution to adaptive optimal control. It is shown that suboptimal controllers can be learned directly from input-state data collected along the trajectories of the robot. Rigorous proofs for the convergence of the novel data-driven value iteration (VI) algorithm and the stability of the closed-loop robot system are provided. Experiments are conducted to demonstrate the efficiency of the novel adaptive suboptimal controller derived from the data-driven VI algorithm in balancing the wheel-legged robot to the equilibrium.

Convex Searches for Discrete-Time Zames–Falb Multipliers

Abstract: In this article, we develop and analyze convex searches for Zames–Falb multipliers. We present two different approaches: infinite impulse response (IIR) and finite impulse response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large-order FIR multiplier. We show that searches in discrete time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell _{2}$ -stability results in the literature for slope-restricted nonlinearities. In particular, we establish the equivalence between the state-of-the-art Lyapunov results for slope-restricted nonlinearities and a subset of the FIR multipliers. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.

Duality bounds for discrete-time Zames-Falb multipliers

Abstract: We develop phase limitations for the discrete-time Zames-Falb multipliers based on the separation theorem for Banach spaces. By contrast with their continuous-time counterparts they lead to numerically efficient results that can be computed either in closed form or via a linear program. The closed-form phase limitations are tight in the sense that we can construct multipliers that meet them with equality. We discuss numerical examples where the limitations are stronger than others in the literature. The numerical results complement searches for multipliers in the literature; they allow us to show, by construction, that the set of plants for which a suitable Zames-Falb multiplier exists is non-convex.