Mesh stability of look-ahead interconnected systems

403 Fig. 4. The response of the performance function J(u). function has almost only one peak. This means that the decreasing direction for the entropy is toward having a narrow shape of the output probability density function. This is in line with the theoretical analysis as a small entropy means the uncertainty of the output is small, which indicates that the shape of the output probability density function is narrow. The response of the performance function is shown in Fig. 4, where it can be seen that a monotonically decreasing of J(u k) has been achieved. This shows the effectiveness of the proposed control algorithm (22). In this note, the entropy concept has been applied to the design of controllers for general stochastic systems subjected to arbitrary bounded random inputs. A linear B-spline model [11] has been used to formulate the system and a performance function which includes the entropy term and a quadratic input constraint. A local optimal control input has been formulated under certain conditions, and it has been shown that the control input is in a form of a nonlinear feedback which is related to the measured output probability density functions of the system and the past inputs. The closed loop stability is analyzed and a local stability condition has been established. A simulated example is used to illustrate the use of the proposed algorithm and encouraging results have been obtained. , " Robust control of the output probability density functions for multivariable stochastic systems, " IEEE Trans. , " On the control of the output probability density functions for a class of nonlinear stochastic systems, " in Proc. Abstract—In this note, we define a notion of mesh stability for a class of interconnected nonlinear systems. Intuitively mesh stability is the property of damping disturbance propagation. We derive a set of sufficient conditions to assure mesh stability of " look-ahead " interconnected systems. Mesh stability is shown to be robust with respect to structural and singular perturbations. The theory is applied to an example of formation flying.