This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity result...This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity results of positive periodic solutions are derived. Our results improve theoremsin the literature.展开更多
In this paper, we develop a trust region algorithm for convex constrained optimizationproblems. Different from the traditional trust region algorithms, our trust region model includesmemory of the past iteration, whic...In this paper, we develop a trust region algorithm for convex constrained optimizationproblems. Different from the traditional trust region algorithms, our trust region model includesmemory of the past iteration, which makes the algorithm more farsighted in the sense that its behav-ior is not completely dominated by the local nature of the objective function. We present a nonmono-tone algorithm that has this feature and prove its global convergence under suitable conditions.展开更多
A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorith...A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorithm which includes two phases is that chaotic behavior is exploited to conduct a rough search of the problem space in order to find the promising individuals in Phase I. Adjustment strategy of steplength and intensive searches in Phase II are employed. The population sequences generated by the algorithm asymptotically converge to global optimal solutions with probability one. The proposed algorithm is applied to several typical test problems. Numerical results illustrate that this algorithm can more efficiently solve complex global optimization problems than evolutionary programming and evolution strategies in most cases.展开更多
Two kinds of saturated controllers are designed for a class of feedforward systems andthe closed-loop resulted is locally input-to-state stable and input-to-state stable, respectively. By theword “locally”, it is me...Two kinds of saturated controllers are designed for a class of feedforward systems andthe closed-loop resulted is locally input-to-state stable and input-to-state stable, respectively. By theword “locally”, it is meant that there are restrictions on the amplitude of inputs. At first, underthe guidance of suitable energy functions, two kinds of saturated controllers are designed as locallyinput-to-state stabilizers for a class of perturbed linear systems, from which explicit gain estimationscan be obtained for the subsequent design. Then under the conditions that two subsystems of thefeedforward system are respectively of locally input-to-state stability and input-to-state stability, thesmall gain theory is used to determine saturated degrees for corresponding robust stabilizers. Thestability proofs are given by using a new characterization of input-to-state stability that is based onthe concept of ultimate boundedness. As an application, saturated controllers are designed for thepartial dynamics of a certain inverted pendulum.展开更多
The paper consists of three topics on control theory and engineering applications, namely bifurcation control, manufacturing planning, and formation control. For each topic, we summarize the control problem to be addr...The paper consists of three topics on control theory and engineering applications, namely bifurcation control, manufacturing planning, and formation control. For each topic, we summarize the control problem to be addressed and some key ideas used in our recent research. Interested readers are referred to related publications for more details. Each of the three topics in this paper is technically independent from the other ones. However, all three parts together reflect the recent research activities of the first author, jointly with other researchers in different fields.展开更多
An iterative adaptive pole placement algorithm is presented. The stability and the convergence of the algorithmare respectively established. Since one-step iterative formulation in computing controller's parameter...An iterative adaptive pole placement algorithm is presented. The stability and the convergence of the algorithmare respectively established. Since one-step iterative formulation in computing controller's parameters is used, the on-line computation cost is greatly reduced with respected to the traditional algorithm. The algorithm with the feed-forward can follow arbitrarily bounded output. The algorithm is also extended to multivariate case. Simulation examples show the efficiency and robustness of the algorithm.展开更多
文摘This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity results of positive periodic solutions are derived. Our results improve theoremsin the literature.
文摘In this paper, we develop a trust region algorithm for convex constrained optimizationproblems. Different from the traditional trust region algorithms, our trust region model includesmemory of the past iteration, which makes the algorithm more farsighted in the sense that its behav-ior is not completely dominated by the local nature of the objective function. We present a nonmono-tone algorithm that has this feature and prove its global convergence under suitable conditions.
文摘A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorithm which includes two phases is that chaotic behavior is exploited to conduct a rough search of the problem space in order to find the promising individuals in Phase I. Adjustment strategy of steplength and intensive searches in Phase II are employed. The population sequences generated by the algorithm asymptotically converge to global optimal solutions with probability one. The proposed algorithm is applied to several typical test problems. Numerical results illustrate that this algorithm can more efficiently solve complex global optimization problems than evolutionary programming and evolution strategies in most cases.
文摘Two kinds of saturated controllers are designed for a class of feedforward systems andthe closed-loop resulted is locally input-to-state stable and input-to-state stable, respectively. By theword “locally”, it is meant that there are restrictions on the amplitude of inputs. At first, underthe guidance of suitable energy functions, two kinds of saturated controllers are designed as locallyinput-to-state stabilizers for a class of perturbed linear systems, from which explicit gain estimationscan be obtained for the subsequent design. Then under the conditions that two subsystems of thefeedforward system are respectively of locally input-to-state stability and input-to-state stability, thesmall gain theory is used to determine saturated degrees for corresponding robust stabilizers. Thestability proofs are given by using a new characterization of input-to-state stability that is based onthe concept of ultimate boundedness. As an application, saturated controllers are designed for thepartial dynamics of a certain inverted pendulum.
基金Supported in part by Ford Motor Company, U.S. Air Force Research Laboratory, and National Science Foundation
文摘The paper consists of three topics on control theory and engineering applications, namely bifurcation control, manufacturing planning, and formation control. For each topic, we summarize the control problem to be addressed and some key ideas used in our recent research. Interested readers are referred to related publications for more details. Each of the three topics in this paper is technically independent from the other ones. However, all three parts together reflect the recent research activities of the first author, jointly with other researchers in different fields.
文摘An iterative adaptive pole placement algorithm is presented. The stability and the convergence of the algorithmare respectively established. Since one-step iterative formulation in computing controller's parameters is used, the on-line computation cost is greatly reduced with respected to the traditional algorithm. The algorithm with the feed-forward can follow arbitrarily bounded output. The algorithm is also extended to multivariate case. Simulation examples show the efficiency and robustness of the algorithm.
