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How to find a minimum phase output in the exact tracking problem for the nonminimum phase underactuated surface ship
No full textVirtual Holonomic Constraints for Euler-Lagrange Systems
No full textThis paper investigates virtual holonomic constraints for Euler-Lagrange systems with n degrees-of-freedom and n - 1 controls. In our framework, a virtual holonomic constraint is a relation specifying n - 1 configuration variables in terms of a single angular configuration variable. The enforcement by feedback of such a constraint induces a desired repetitive behavior in the system. We give conditions under which a virtual holonomic constraint is feasible, i.e, it can be made invariant by feedback, and it is stabilizable. We provide sufficient conditions under which the dynamics on the constraint manifold correspond to an Euler- Lagrange system. These ideas are applied to the problem of swinging up an underactuated pendulum while guaranteeing that the second link does not fall over
A minimum phase output in the exact tracking problem for the nonminimum phase underactuated surface ship
No full textGeneralized Bang-Bang Control for Feedforward Constrained Regulation
No full textIn the behavioral framework for continuous-time linear scalar systems, simple sufficient conditions for the solution of the minimum-time rest-to-rest feedforward constrained control problem are provided. The investigation of the time-optimal input–output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure. The resulting optimal input is composed of sequences of bang–bang functions and linear combinations of the modes associated to the zero dynamics. This signal behavior constitutes a generalizedbang–bang control that can be fruitfully exploited for feedforward constrained regulation. Using discretization, an arbitrarily good approximation of the optimal generalizedbang–bang control is found by solving a sequence of linear programming problems. Numerical examples are included
On the complexity of quadratic programming with two quadratic constraints
Full text linkThe complexity of quadratic programming problems with two quadratic constraints is an open problem. In this paper we show that when one constraint is a ball constraint and the Hessian of the quadratic function defining the other constraint is positive definite, then, under quite general conditions, the problem can be solved in polynomial time in the real-number model of computation through an approach based on the analysis of the dual space of the Lagrange multipliers. However, the degree of the polynomial is rather large, thus making the result mostly of theoretical interest
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