Michael Cantoni

Michael Cantoni, Farhad Farokhi, Eric C. Kerrigan et al.

A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure of performance, are all separable with respect to the spatial dimension of the underlying cascade of sub-systems, as well as the temporal dimension of the dynamics. By virtue of this structure, the computation cost of an interior-point method for an equivalent quadratic programming formulation of the optimal control problem can be made to scale linearly with the number of sub-systems. However, the complexity of this approach grows cubically with the time horizon. As such, computational advantage becomes apparent in situations where the number of sub-systems is relatively large. In any case, the method is amenable to distributed computation with low communication overhead and only immediate upstream neighbour sharing of partial model data among processing agents. An example is presented to illustrate an application of the main results to model data for the cascade dynamics of an automated irrigation channel.

Farhad Farokhi, Iman Shames, Michael Cantoni

Consider a group of effort-averse, or lazy, sensors that seek to minimize the effort invested to collect measurements of a variable. Increasing the effort invested by the sensors improves the quality of the measurements provided to the central planner but this incurs increased costs to the sensors. The central planner, which processes the sensor measurements, employs an averaging estimator. It also determines contracts for rewarding sensors based on the measurements obtained. The problem of designing a contract that yields an estimation-error based quality-of-service level in return for the reward extended to sensors is investigated in this paper. To this end, a game is formulated between the central planner and the sensors. Conditions for the existence and uniqueness of an equilibrium are identified. The equilibrium is constructed explicitly and its properties in response to a reward based contract are studied. It turns out that the central planner, while not being able to directly measure the effort invested by the sensors, can enhance the estimation quality by rewarding each sensor based on the distance of its measurements from the output of the averaging estimator. Ultimately, optimal contracts are designed from the perspective of the budget required for achieving a specified level of estimation error.

Farhad Farokhi, Iman Shames, Michael Cantoni

In this paper, the interplay between a class of nonlinear estimators and strategic sensors is studied in several participatory-sensing scenarios. It is shown that for the class of estimators, if the strategic sensors have access to noiseless measurements of the to-be-estimated-variable, truth-telling is an equilibrium of the game that models the interplay between the sensors and the estimator. Furthermore, performance of the proposed estimators is examined in the case that the strategic sensors form coalitions and in the presence of noise.

Jintao Sun, Michael Cantoni

Standard formulations of prescribed worst-case disturbance energy-gain control policies for linear time-varying systems depend on all forward model data. In discrete time, this dependence arises through a backward Riccati recursion. This article is about the infinite-horizon $\ell_2$ gain performance of state feedback policies with only finite receding-horizon preview of the model parameters. The proposed synthesis of controllers subject to such a constraint leverages the strict contraction of lifted Riccati operators under uniform controllability and observability. The main approximation result is a sufficient number of preview steps for the incurred performance loss to remain below any set tolerance, relative to the baseline gain bound of the associated infinite-preview controller. Aspects of the result are explored in a numerical example.

Julian Tran, Farhad Farokhi, Michael Cantoni et al.

This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier's homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast.

Farhad Farokhi, Michael Cantoni, Iman Shames

We consider load scheduling on constrained continuous-time linear dynamical systems, such as automated irrigation and other distribution networks. The requested loads are rigid, i.e., the shapes cannot be changed. Hence, it is only possible to shift the order back-and-forth in time to arrive at a feasible schedule. We present a numerical algorithm based on using log-barrier functions to include the state constraints in the social cost function (i.e., an appropriate function of the scheduling delays). This algorithm requires a feasible initialization. Further, in another algorithm, we treat the state constraints as soft constraints and heavily penalize the constraint violations. This algorithm can even be initialized at an infeasible point. The applicability of both these numerical algorithms is demonstrated on an automated irrigation network with two pools and six farms.