One of the growing areas of application of embedded systems in robotics, aerospace, military, etc. is autonomous mobile systems. Usually, such embedded systems have multitask multimodal workloads. These systems must sustain the required performance of their dynamic workloads in presence of varying power budget due to rechargeable power sources, varying die temperature due to varying workloads and/or external temperature, and varying hardware resources due to occurrence of hardware faults. This paper proposes a run-time decision-making method, called Decision Space Explorer, for FPGA-based Systems-on-Chip (SoCs) to support changing workload requirements while simultaneously mitigating unpredictable variations in power budget, die temperature, and hardware resource constraints. It is based on the concept of Run-Time Structural Adaptation (RTSA); whenever there is a change in a system’s set of constraints, Explorer selects a suitable hardware processing circuit for each active task at an appropriate operating frequency such that all the constraints are satisfied. Explorer has been experimentally deployed on the ARM Cortex-A9 core of Xilinx Zynq XC7Z020 SoC. Its worst-case decision-making time for different scenarios ranges from tens to hundreds of microseconds. Explorer is thus suitable for enabling RTSA in systems where specifications of multiple objectives must be maintained simultaneously, making them self-sustainable.