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Meeting temperature constraints and reducing the hot-spots are critical for achieving reliable and efficient operation of complex multi-core systems. In this paper we aim at achieving an online smooth thermal control action that minimizes the performance loss as well as the computational and hardware overhead of embedding a thermal management system inside the MPSoC. The optimization problem considers the thermal profile of the system, its evolution over time and current time-varying workload requirements. We formulate this problem as a discrete-time control problem using model predictive control. The solution is computed off-line and partially on-line using an explicit approximate algorithm. This proposed method, compared with the optimum approach provides a significant reduction in hardware requirements and computational cost at the expense of a small loss in accuracy. We perform experiments on a …