Populations of neurons in motor cortex engage in complex transient dynamics of large amplitude during the execution of limb movements. Traditional network models with stochastically assigned synapses cannot reproduce this behavior. Here we introduce a class of cortical architectures with strong and random excitatory recurrence that is stabilized by intricate, fine-tuned inhibition, optimized from a control theory perspective. Such networks transiently amplify specific activity states and can be used to reliably execute multidimensional movement patterns. Similar to the experimental observations, these transients must be preceded by a steady-state initialization phase from which the network relaxes back into the background state by way of complex internal dynamics. In our networks, excitation and inhibition are as tightly balanced as recently reported in experiments across several brain areas, suggesting inhibitory control of complex excitatory recurrence as a generic organizational principle in cortex.