In this work we propose a new formulation of the stochastic based minimum back-off operating point selection problem. It is shown that this formulation has a convex/reverse-convex form and is thus readily solved globally via a branch and bound search scheme. The formulation is then extended to the partial state information case as well as the discrete-time framework. The formulation is unique in that the controller feedback gain is not specified a priori but rather is to be determined by the proposed optimization. It is further shown that the obtained feedback gain is such that an LQR inverse optimal feedback is guaranteed to exist within the set of feasible feedback gains. A postprocessing procedure is proposed for the synthesis of such a feedback as well as the corresponding LQR objective function weights. This connection between the economics of operating point selection and the dynamics of predictive controller tuning (i.e., the selection of objective function weighs) is expected to significantly enhance the synergy of modern hierarchial control structures. The proposed method is illustrated, first through a simple massspring-damper example and then via a 3 input, 4 state furnace/reactor system.

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In this article, we propose a new method for the selection of control system hardware (sensors and actuators) for distributed parameter systems. The proposed design scheme seeks to minimize the capital cost of hardware while satisfying predefined performance constraints. Within this minimum capital cost framework, three design scenarios will be discussed; the closedloop full state information actuator selection problem, the open-loop partial state information sensor selection problem, and the closed-loop partial state information simultaneous sensor and actuator selection problem. The proposed method will be illustrated through application to a nonisothermal tubular reactor example.

Recently, a number of covariance-constrained hardware selection problems have been proposed. However, underlying each is the choice of a compensating element (i.e., the state estimator for the sensor case, the feedback controller for the actuator case, and both for the simultaneous case). The subtlety is whether these compensators should be optimal or suboptimal. In this paper, we present formulations using both types of compensators and then prove that the global solution for each type of formulation is independent of the compensator assumption. However, in spite of this equivalence of solutions, the computational perspective indicates that one choice will always have an advantage. While the computational difference is minor in the sensor selection case, significant advantages can be found in the suboptimal controller version of the actuator selection problem. In particular, the suboptimal version can be used to find global solutions to the previously intractable optimal controller formulation. In the simultaneous case, similar results are presented and lead to the first global solution scheme for the covariance-based simultaneous sensor and actuator selection problem.

A new formulation of the actuator placement problem is presented. This formulation considers capital cost in the objective function and highlights the importance of magnitude limits on both input and output signals through variance bounding constraints on each. Thus, the proposed optimization problem is aimed at finding the set of minimum cost actuator arrays such that there exists a linear feedback for which all closed-loop signals will satisfy their magnitude limits. The original formulation of this problem results in a Mixed Integer Nonlinear Program (MINLP). However, through an LMI based transformation we exactly convert the problem into a computationally advantageous Mixed Integer Convex Program (MICP). Finally, the design method is applied to an example of actuator placement in a non-isothermal tubular reactor.