Simplified optimized control using reinforcement learning algorithm for a class of stochastic nonlinear systems

This article proposes a novel robust control strategy for three-phase power converters operated under unbalanced grid conditions. A consolidated control objective is obtained in the stationary $\alpha \beta$ frame, which can be flexibly adjusted according to the degree of oscillation in the active and reactive powers and the balance of the three-phase current. Based on the dynamics of the converter and control objective, a control scheme in a cascaded framework is presented, in which an adaptive observer is applied to estimate the positive and negative sequences of the grid voltage. In the current tracking loop, a super-twisting algorithm current controller coupled with a super-twisting differentiator is implemented to track the current references, featuring rapid dynamics, and improved robustness. Additionally, in the voltage regulation loop, an effective composite controller is developed to regulate the dc-link voltage, where a super-twisting observer is used to estimate the load disturbance, thereby improving the performance of the converter. The experimental results are provided to confirm the effectiveness and superiority of the proposed control strategy.

Observer-Based Sliding-Mode Control for Grid-Connected Power Converters Under Unbalanced Grid Conditions

In this article, an optimized leader-follower consensus control is proposed for a class of second-order unknown nonlinear dynamical multiagent system. Different with the first-order multiagent consensus, the second-order case needs to achieve the agreement not only on position but also on velocity, therefore this optimized control is more challenging and interesting. To derive the control, reinforcement learning (RL) can be a natural consideration because it can overcome the difficulty of solving the Hamilton–Jacobi–Bellman (HJB) equation. To implement RL, it needs to iterate both adaptive critic and actor networks each other. However, if this optimized control learns RL from most existing optimal methods that derives the critic and actor adaptive laws from the negative gradient of square of the approximating function of the HJB equation, this control algorithm will be very intricate, because the HJB equation correlated to a second-order nonlinear multiagent system will become very complex due to strong state coupling and nonlinearity. In this work, since the two RL adaptive laws are derived via implementing the gradient descent method to a simple positive function, which is obtained on the basis of a partial derivative of the HJB equation, this optimized control is significantly simple. Meanwhile, it not merely can avoid the requirement of known dynamic acknowledge, but also can release the condition of persistent excitation, which is demanded in most RL optimization methods for training the adaptive parameter more sufficiently. Finally, the proposed control is demonstrated by both theory and computer simulation.

Optimized Leader-Follower Consensus Control Using Reinforcement Learning for a Class of Second-Order Nonlinear Multiagent Systems

Cauchy–Schwarz norm inequalities for weak∗-integrals of operator valued functions

Trace inequalities for sums and products of matrices are pre-
sented. Relations between the given inequalities and earlier results are dis-
cussed. Among other inequalities it is shown that if A and B are positive
semidenite matrices, then
tr (AB)k min

kAkk trBk; kBkk trAk

for any positive intger k.

DOI: 10.1017/S0004972712000627

/pdf/trace-inequalities-for-matrices-4q8sp4hv57.pdf

Trace inequalities for matrices

Let p, q > 0 satisfy 1/p + 1/q = 1. We prove that for any pair A, B of n × n complex matrices there is a unitary matrix U, depending on A, B, such that

$$U*\left| {AB*} \right|U \leqslant {\left| A \right|^p}/p + {\left| B \right|^q}/q.$$

Matrix Young Inequalities

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Matrix Young Inequalities