A HVAC system for a building includes a plant and a plurality of single-variable extremum-seeking controllers (ESCs). The plant includes HVAC equipment operable to affect an environmental condition in the building. Each of the single-variable ESCs is configured to perturb a different manipulated variable with a different excitation signal and provide the manipulated variables as perturbed inputs to the plant. The plant uses multiple perturbed inputs to concurrently affect a performance variable. The single-variable ESCs are configured to estimate a gradient of the performance variable with respect to the each manipulated variable and independently drive the gradients toward zero by independently modulating the manipulated variables.