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This paper investigates the spacecraft rendezvous problem with the target spacecraft on an arbitrary elliptical orbit. The relative motion of two spacecrafts is established based on the T-H equations. In order to avert some time-varying model parameters, a variable transformation approach is introduced to obtain the new state-space equations. Then, the control laws are designed based on backstepping method. With the analysis by a Lyapunov approach, the proposed control laws can guarantee the asymptotic stability of the closed-loop system and are also optimal with respect to a certain performance index, simulation results are presented to illustrate the effectiveness of the proposed approach.

A direct robust adaptive nonlinear control scheme for a class of uncertain nonlinear Markovian jump systems with nonlinear state-dependent uncertainty is presented. The proposed scheme is Lyapunov-based and guarantees the global uniform ultimate boundedness of the closed-loop system in the mean sense. A numerical example is given to demonstrate the validity of the results.

Robust LQG problems of discrete-time Markovian jump systems with uncertain noises are investigated. The problem addressed is the construction of perturbation upper bounds on the uncertain noise covariances so as to guarantee that the deviation of the control performance remains within the precision prescribed in actual problems. Furthermore, this regulator is capable of minimizing the worst performance in an uncertain case. A numerical example is exploited to show the validity of the method.

Cao's work shows that, by defining an α-dependent equivalent infinitesimal generator Aα, a semi-Markov decision process (SMDP) with both average- and discounted-cost criteria can be treated as an α-equivalent Markov decision process (MDP), and the performance potential theory can also be developed for SMDPs. In this work, we focus on establishing error bounds for potential and Aα-based iterative optimization methods. First, we introduce an α-uniformized Markov chain (UMC) for a SMDP via Aα and a uniformized parameter, and show their relations. Especially, we obtain that their performance potentials, as solutions of corresponding Poisson equations, are proportional, so that the studies of a SMDP and the α-UMC based on potentials are unified. Using these relations, we derive the error bounds for a potential-based policy-iteration algorithm and a value-iteration algorithm, respectively, when there exist various calculation errors. The obtained results can be applied directly to the special models, i.e., continuous-time MDPs and Markov chains, and can be extended to some simulation-based optimization methods such as reinforcement learning and neurodynamic programming, where estimation errors or approximation errors are common cases. Finally, we give an application example on the look-ahead control of a conveyor-serviced production station (CSPS), and show the corresponding error bounds.

A modular approach of the estimation-based design in adaptive linear control systems has been extended to the adaptive robust control of strict-feedback stochastic nonlinear systems with additive standard Wiener noises and constant unknown parameters. By using Ito’s differentiation rule, nonlinear damping and adaptive Backstepping procedure, the input-to-state stable controller of global stabilization in probability is developed, which guarantees that system states are bounded and the system has a robust stabilization. According to Swapping technique, we develop two filters and convert dynamic parametric models into static ones to which the gradient update law is designed. Transient performance of the system is estimated by the norm of error. Results of simulation show the effectiveness of the control algorithms. The modular design, which has a concise hierarchy, is more flexible and versatile than a Lyapunov-based algorithm.

The optimization problems of Markov control processes (MCPs) with exact knowledge of system parameters, in the form of transition probabilities or infinitesimal transition rates, can be solved by using the concept of Markov performance potential which plays an important role in the sensitivity analysis of MCPs. In this paper, by using an equivalent infinitesimal generator, we first introduce a definition of discounted Poisson equations for semi-Markov control processes (SMCPs), which is similar to that for MCPs, and the performance potentials of SMCPs are defined as solution of the equation. Some related optimization techniques based on performance potentials for MCPs may be extended to the optimization of SMCPs if the system parameters are known with certainty. Unfortunately, exact values of the distributions of the sojourn times at some states or the transition probabilities of the embedded Markov chain for a large-scale SMCP are generally difficult or impossible to obtain, which leads to the uncertainty of the semi-Markov kernel, and thereby to the uncertainty of equivalent infinitesimal transition rates. Similar to the optimization of uncertain MCPs, a potential-based policy iteration method is proposed in this work to search for the optimal robust control policy for SMCPs with uncertain infinitesimal transition rates that are represented as compact sets. In addition, convergence of the algorithm is discussed.

Average-cost optimization problems for a class of continuous-time Markov control processes with a compact action set have been studied. The definition of a generalized average-cost Poisson equation, which can be viewed as an extension to the standard one is first given. Markov performance potentials are defined as its unique solution. Based on the formula of performance potentials, an average-cost optimality equation is derived and the existence of its solution is established. Then, policy iteration and value iteration algorithms are proposed and their convergence discussed. A numerical example for controlled closed queuing networks illustrates the application of the proposed value iteration algorithm.

In this paper, the concept of the infinitesimal realization factor is extended to the parameter-dependent performance functions in closed queueing networks. Then the concepts of realization matrix (its elements are called realization factors) and performance potential are introduced, and the relations between infinitesimal realization factors and these two quantities are discussed. This provides a united framework for both IPA and non-IPA approaches. Finally, another physical meaning of the service rate is given.