In this work, we introduce brain-inspired neural circuitries (BINC) which are learned to generate a desired behavior and perform control tasks. A fundamental method in the design of new artificial intelligence (AI) systems is to look into the ways brains process information, and create an artificial version of this mechanism. Inspired by the way real neurons relationally form communication in nervous systems, we formulate relational policies called Design Operators (DO) and define them as the basis of signaling between two neurons. DOs include excitation, sequencing and coupling, amongst others. With the use of DOs, within a simulated platform where neurons are deterministically modeled by ordinary differential equations, we design verifiable neural networks which are able to translate parallel sensory information to motor actions. DO-based networks form the essential substrate for producing a specific behavior. However, parameters of the network have to be learned to express the actual behavior. In this regard, we introduce a novel search-based learning algorithm which is founded by a Monte Carlo memetic learning technique for parameter optimization. We set up two robot control experiments to assess the performance of our networks. I) Autonomous parallel parking of a rover robot II) Control of an industrial arm robot. DO-based networks are designed and learned for each of the tasks. In contrast to many deep learning-based agents for a similar objective, our networks substantially require fewer number of neurons, their working principles can be verified, and they are highly resilient to noise attacks. We quantify such properties throughly. Moreover, we show how complex behavior get originated form simple neural circuit topologies. Within our simulation platform, We take a biological neural circuit and reconfigure its parameters to function as the controller for our parking task. This is called "Re-purposing the objective of a network". We see that this Re-purposed network compared to DO-based networks, learns to perform a sequence of tasks with the use of single neurons rather than a group of neurons. Finally, we develop an end-to-end platform for automatically generating neural circuits, given an objective for a control task. Starting from an fully-connected network topology, a modern model reduction technique is applied to realize minimal circuits for the specific control task. This setting is employed as an early-stage analysis step, in the design of a DO-based network, as well as for the end-stage, to evaluate the quality of the exhibited behavior by the controller.