This paper investigates the use of canonical piecewise affine (PWA) functions for approximation and fast implementation of linear MPC controllers. The control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest. The stability properties of the resulting closed-loop system are analyzed by constructing a suitable PWA Lyapunov function. The main advantage of the proposed approach to the implementation of MPC controllers is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds

SUMMARYDigital architectures for the circuit realization of multivariate piecewise-linear (PWL) functions are reviewed and compared. The output of the circuits is a digital word representing the value of the PWL function at the n-dimensional input. In particular, we propose two architectures with different levels of parallelism/complexity. PWL functions with n = 3 inputs are implemented on an FPGA and experimental results are shown. The accuracy in the representation of PWL functions is tested through three benchmark examples, two concerning three-variate static functions and one concerning a dynamical control system defined by a bi-variate PWL function.

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This brief proposes a digital circuit architecture implementing a class of continuous piecewise-affine (PWA) functions. The work rests on a previous architecture realizing PWA functions with uniform resolution. By using PWA mapping that can be implemented through a few simple functional blocks, it is possible to extend the representation capabilities of the architecture to PWA functions with nonuniform resolution. After defining the mapping and the corresponding functional blocks, the proposed architecture is implemented in a field-programmable gate array, and a simple example is shown.