Large language models (LLMs) are increasingly being explored in cyber-physical system design as a promising tool to facilitate the conversion of natural-language requirements into formal specifications, and the generation of plans and controllers that provably satisfy them. Existing LLM-based pipelines, however, mostly validate the designed controllers by simulation, and carry no mechanism for improving their outcomes from past designs. We present ACIES, a self-evolving agentic contract-based framework for cyber-physical system control synthesis. Given a set of system requirements, ACIES automatically generates a control architecture that realizes the requirements using a sequence of synthesis episodes. Within each episode, a Translator agent formalizes the system requirements into temporal logic, and a Decomposer agent structures them into a system-level contract and proposes a decomposition into component-level contracts that can be independently implemented. A formal verification step is then integrated in the decomposition loop to check whether the component-level contracts are consistent, compatible, and provide a correct refinement of the system-level contract. Each failed check, at the verification or implementation step, returns a diagnostic signal that drives automated contract repair at the system or the component level. Across episodes, a Summarizer agent distills verification outcomes into reusable lessons stored in a memory. Evaluation results on five control synthesis tasks with eight LLM backbones show that the formalized system requirements are successfully decomposed and mapped to a synthesizable control architecture that realizes them, while self-evolution reduces the Decomposer token consumption by up to 65% and the end-to-end synthesis latency by up to 62%.