text: We consider a joint sensor and controller design problem for linear Gaussian stochastic systems in which a weighted sum of quadratic control cost and the amount of information acquired by the sensor is minimized. This problem formulation is motivated by situations where a control law must be designed in the presence of sensing, communication, and privacy constraints. We show that the optimal joint sensor-controller design is relatively easy when the sensing policy is restricted to be linear. Namely, an explicit form of the optimal linear sensor equation, the Kalman filter, and the certainty equivalence controller that jointly solves the problem can be efficiently found by semidefinite programming (SDP). Whether the linearity assumption in our design is restrictive or not is currently an open problem.
  @cite_26: 
  @cite_13: Abstract We consider stochastic dynamic decision problems where at each step two consecutive decisions must be taken, one being what information bearing signal(s) to transmit and the other what control action(s) to exert. For finite-horizon problems involving first-order ARMA models with Gaussian statistics and a quadratic cost criterion, we show that the optimal measurement strategy consists of transmitting the innovation linearly at each stage, which in turn leads to optimality of a linear control law. We then extend this result to infinite-horizon models with discounted costs, showing optimality of linear designs. Subsequently, we show that these appealing results do not necessarily carry over to higher order ARMA models, for which we first characterize the best designs within the affine class, and then derive instances of the problem for which there exist non-linear designs that outperform the optimal designs within the affine class. The paper also includes some illustrative numerical examples on the different classes of problems considered.
  @cite_17: This paper studies the optimization of observation channels (stochastic kernels) in partially observed stochastic control problems. In particular, existence and continuity properties are investigated, mostly (but not exclusively) concentrating on the single-stage case. Continuity properties of the optimal cost in channels are explored under total variation, setwise convergence, and weak convergence. Sufficient conditions for compactness of a class of channels under total variation and setwise convergence are presented, and applications to quantization are explored.
summary: However, the majority of the existing work in this context assume sensor models and or channel models , and are different from ). A few exceptions include @cite_13 and @cite_26 , where sensor-controller joint design problems are considered. However, these works are concerned with sensor power constraints rather than information constraints, and are different from ). Our problem formulation ) falls into a general class of sensor optimization problems considered in @cite_17 , where several results are derived regarding the convexity of the problem and the existence of an optimal solution under different choices of topologies in the space of sensors. However, no structural results on specific problems appear there.